Groups and group theory Books
Creative Media Partners, LLC On Metabelian Groups
£21.80
Springer Abels Theorem in Problems and Solutions Based on the Lectures of Professor V I Arnold The Kluwer International Series in Engineering Computer Science
Book SynopsisFrom the contents:Preface for the English edition; V.I. Arnold.- Preface.- Introduction.- 1: Groups.- 2: The complex numbers.- 3: Hints, Solutions and Answers.- Appendix. Solvability of equations by explicit formulae; A. Khovanskii.- Bibliography.- Appendix; V.I. Arnold.- Index. Trade ReviewFrom the reviews: "This very special and brilliant text has been written for bright non-specialists in mathematics, but it leads the reader up to topical research problems in the field, and that in a masterly manner. The book is absolutely self-contained, in its own particular fashion, and it is therefore perfectly suited for self-study, ranging from advanced high school to graduate level. No doubt, the thorough and serious working with this outstanding text could turn very beginners into creative almost-experts in the field." (Werner Kleinert, Zentralblatt MATH, Vol. 1065 (16), 2005)Table of ContentsPreface for the English edition; V.I. Arnold. Preface. Introduction. 1: Groups. 1.1. Examples. 1.2. Groups of transformations. 1.3. Groups. 1.4. Cyclic groups. 1.5. Isomorphisms. 1.6. Subgroups. 1.7. Direct product. 1.8. Cosets. Lagrange's theory. 1.9. Internal automorphisms. 1.10. Normal subgroups. 1.11. Quotient groups. 1.12. Commutant. 1.13. Homomorphisms. 1.14. Soluble groups. 1.15. Permutations. 2: The complex numbers. 2.1. Fields and polynomials. 2.2. The field of complex numbers. 2.3. Uniqueness of the field of complex numbers. 2.4. Geometrical descriptions of the field of complex numbers. 2.5. The trigonometric form of the complex numbers. 2.6. Continuity. 2.7. Continuous curves. 2.8. Images of curves: the basic theorem of the algebra of complex numbers. 2.9. The Riemann surface of the function w = SQRTz. 2.10. The Riemann surfaces of more complicated functions. 2.11. Functions representable by radicals. 2.12. Monodromy groups of multi-valued functions. 2.13. Monodromy groups of functions representable by radicals. 2.14. The Abel theorem. 3: Hints, Solutions and Answers. 3.1.Problems of Chapter 1. 3.2. Problems of Chapter 2. Drawings of Riemann surfaces; F. Aicardi. Appendix. Solvability of equations by explicit formulae; A. Khovanskii. A.1. Explicit solvability of equations. A.2. Liouville's theory. A.3. Picard-Vessiot's theory. A.4. Topological obstructions for the representation of functions by quadratures. A.5. S-functions. A.6. Monodromy group. A.7. Obstructions for the representability of functions by quadratures. A.8. Solvability of algebraic equations. A.9. The monodromy pair. A.10. Mapping of the semi-plane to a polygon bounded by arcs of circles. A.11. Topological obstructions for the solvability of differential equations. A.12. Algebraic functions of several variables. A.13. Functions of several complex variables representable by quadratures and generalized quadratures. A.14. SC-germs. A.15. Topological obstruction for the solvability of the holonomic systems of linear differential equations. A.16. Topological obstruction for the solvability of the holonomic systems of linear differential equations. Bibliography. Appendix; V.I. Arnold. Index.
£113.99
Springer New York Topological Methods in Group Theory
Book SynopsisThis book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field.Trade ReviewFrom the reviews:"The author of this book has done a great service to the geometric group theory community by writing a very useful and well-written book on many topics in geometric group theory that every neophyte and researcher in the field should know. … This book is suitable as a textbook for a graduate course, with many good examples and exercises. The reviewer highly recommends this book as a basic reference book for topological methods in group theory." (John G. Ratcliffe, Mathematical Reviews, Issue 2008 j)"This is an interesting book on the interplay between algebraic topology and the theory of infinite discrete groups written for graduate students and group theorists who need to learn more in geometric and homological group theory. … It is a beautiful text in algebraic topology, with modern topics and which points the reader towards new research directions." (Corina Mohorianu, Zentralblatt MATH, Vol. 1142, 2008)“This book is an invaluable resource for anyone wanting a deep understanding of topics related to the ends of groups. … there is a good deal of material in this book that does not appear anywhere else in the literature. … Geoghegan’s book provides a well-presented, concrete development of geometric group theory focused on a topological approach.” (John Meier, Bulletin of the American Mathematical Society, July, 2012)Table of ContentsAlgebraic Topology for Group Theory.- CW Complexes and Homotopy.- Cellular Homology.- Fundamental Group and Tietze Transformation.- Some Techniques in Homotopy Theory.- Elementary Geometric Topology.- Finiteness Properties of Groups.- The Borel Construction and Bass-Serre Theory.- Topological Finiteness Properties and Dimension of Groups.- Homological Finiteness Properties of Groups.- Finiteness Properties of Some Important Groups.- Locally Finite Algebraic Topology for Group Theory.- Locally Finite CW Complexes and Proper Homotopy.- Locally Finite Homology.- Cohomology of CW Complexes.- Topics in the Cohomology of Infinite Groups.- Cohomology of Groups and Ends of Covering Spaces.- Filtered Ends of Pairs of Groups.- Poincaré Duality in Manifolds and Groups.- Homotopical Group Theory.- The Fundamental Group At Infinity.- Higher homotopy theory of groups.- Three Essays.- Three Essays.
£54.99
Springer Basic Algebra Groups Rings And Fields
Book Synopsis1. Sets.- 2. Groups.- 3. Lattices and Categories.- 4. Rings and Modules.- 5. Algebras.- 6. Multilinear Algebra.- 7. Field Theory.- 8. Quadratic Forms and Ordered Fields.- 9. Valuation Theory.- 10. Commutative Rings.- 11. Infinite Field Extensions.- List of Notations.- Author Index.Trade ReviewFrom the reviews: "The book is a wonderful piece of work that condenses and transmits the long experience of an excellent teacher. The reader enjoys the structure of the precisely designed volume and the beautiful combination of clear arguments and well-chosen examples. A lot of exercises help the reader to deepen his knowledge. This updated and improved introduction to abstract algebra must be on the bookshelves of all algebraists and of all students interested in algebra." (Maria B. Szendrei, Acta Scientiarum Mathematicarum, Vol. 71, 2005) "This is a coherent overview of group, ring and field theory which combines brevity with elegance and authority. … to the serious algebraists and departmental libraries … this book will be an automatic purchase." (Gerry Leversha, The Mathematical Gazette, March, 2005) "This book … is a new and revised version of the author’s famous text ‘Algebra’ … . The book contains numerous exercises, and … many illuminating comments on the subject. There is no doubt that the book will take the position of its predecessor in being one of the most outstanding introductory algebra textbooks." (EMS Newsletter, June, 2004) "The entire text is profusely supported by worked examples. Each section in the book comes with a plentiful supply of carefully selected exercises, and there are also numerous historical remarks and hints for further reading. Altogether, this textbook breathes once more the author’s rich teaching experience and his masterly skill as a textbook writer. … the author has kept his well-tried methodical principle of combining old and new viewpoints in algebra in a natural way, which makes his textbooks so unique, matchless and timelessly valuable." (Werner Kleinert, Zentralblatt MATH, Vol. 1003 (3), 2003)Table of ContentsPreface.- Conventions on Terminology.- Sets.- Groups.- Lattices and Categories.- Rings and Modules.- Algebras.- Multilinear Algebra.- Field Theory.- Quadratic Forms and Ordered Fields.- Valuation Theory.- Commutative Rings.- Infinite Field Extensions.- Bibliography.- List of Notations.- Author Index.- Subject Index.
£71.99
Springer New York Semigroups of Linear Operators and Applications to Partial Differential Equations 44 Applied Mathematical Sciences
Book SynopsisSince the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations.Trade ReviewFrom the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of the London Mathematical Society#2Table of Contents1 Generation and Representation.- 1.1 Uniformly Continuous Semigroups of Bounded Linear Operators.- 1.2 Strongly Continuous Semigroups of Bounded Linear Operators.- 1.3 The Hille-Yosida Theorem.- 1.4 The Lumer Phillips Theorem.- 1.5 The Characterization of the Infinitesimal Generators of C0 Semigroups.- 1.6 Groups of Bounded Operators.- 1.7 The Inversion of the Laplace Transform.- 1.8 Two Exponential Formulas.- 1.9 Pseudo Resolvents.- 1.10 The Dual Semigroup.- 2 Spectral Properties and Regularity.- 2.1 Weak Equals Strong.- 2.2 Spectral Mapping Theorems.- 2.3 Semigroups of Compact Operators.- 2.4 Differentiability.- 2.5 Analytic Semigroups.- 2.6 Fractional Powers of Closed Operators.- 3 Perturbations and Approximations.- 3.1 Perturbations by Bounded Linear Operators.- 3.2 Perturbations of Infinitesimal Generators of Analytic Semigroups.- 3.3 Perturbations of Infinitesimal Generators of Contraction Semigroups.- 3.4 The Trotter Approximation Theorem.- 3.5 A General Representation Theorem.- 3.6 Approximation by Discrete Semigroups.- 4 The Abstract Cauchy Problem.- 4.1 The Homogeneous Initial Value Problem.- 4.2 The Inhomogeneous Initial Value Problem.- 4.3 Regularity of Mild Solutions for Analytic Semigroups.- 4.4 Asymptotic Behavior of Solutions.- 4.5 Invariant and Admissible Subspaces.- 5 Evolution Equations.- 5.1 Evolution Systems.- 5.2 Stable Families of Generators.- 5.3 An Evolution System in the Hyperbolic Case.- 5.4 Regular Solutions in the Hyperbolic Case.- 5.5 The Inhomogeneous Equation in the Hyperbolic Case.- 5.6 An Evolution System for the Parabolic Initial Value Problem.- 5.7 The Inhomogeneous Equation in the Parabolic Case.- 5.8 Asymptotic Behavior of Solutions in the Parabolic Case.- 6 Some Nonlinear Evolution Equations.- 6.1 Lipschitz Perturbations of Linear Evolution Equations.- 6.2 Semilinear Equations with Compact Semigroups.- 6.3 Semilinear Equations with Analytic Semigroups.- 6.4 A Quasilinear Equation of Evolution.- 7 Applications to Partial Differential Equations—Linear Equations.- 7.1 Introduction.- 7.2 Parabolic Equations—L2 Theory.- 7.3 Parabolic Equations—Lp Theory.- 7.4 The Wave Equation.- 7.5 A Schrödinger Equation.- 7.6 A Parabolic Evolution Equation.- 8 Applications to Partial Differential Equations—Nonlinear Equations.- 8.1 A Nonlinear Schröinger Equation.- 8.2 A Nonlinear Heat Equation in R1.- 8.3 A Semilinear Evolution Equation in R3.- 8.4 A General Class of Semilinear Initial Value Problems.- 8.5 The Korteweg-de Vries Equation.- Bibliographical Notes and Remarks.
£151.99
Springer New York An Introduction to the Theory of Groups
Book Synopsis1 Groups and Homomorphisms.- Permutations.- Cycles.- Factorization into Disjoint Cycles.- Even and Odd Permutations.- Semigroups.- Groups.- Homomorphisms.- 2 The Isomorphism Theorems.- Subgroups.- Lagrange's Theorem.- Cyclic Groups.- Normal Subgroups.- Quotient Groups.- The Isomorphism Theorems.- Correspondence Theorem.- Direct Products.- 3 Symmetric Groups and G-Sets.- Conjugates.- Symmetric Groups.- The Simplicity of An.- Some Representation Theorems.- G-Sets.- Counting Orbits.- Some Geometry.- 4 The Sylow Theorems.- p-Groups.- The Sylow Theorems.- Groups of Small Order.- 5 Normal Series.- Some Galois Theory.- The Jordan-Hölder Theorem.- Solvable Groups.- Two Theorems of P. Hall.- Central Series and Nilpotent Groups.- p-Groups.- 6 Finite Direct Products.- The Basis Theorem.- The Fundamental Theorem of Finite Abelian Groups.- Canonical Forms; Existence.- Canonical Forms; Uniqueness.- The KrullSchmidt Theorem.- Operator Groups.- 7 Extensions and Cohomology.- The Extension Problem.- Automorphism Groups.- Semidirect Products.- Wreath Products.- Factor Sets.- Theorems of Schur-Zassenhaus and Gaschütz.- Transfer and Burnside's Theorem.- Projective Representations and the Schur Multiplier.- Derivations.- 8 Some Simple Linear Groups.- Finite Fields.- The General Linear Group.- PSL(2, K).- PSL(m, K).- Classical Groups.- 9 Permutations and the Mathieu Groups.- Multiple Transitivity.- Primitive G-Sets.- Simplicity Criteria.- Affine Geometry.- Projective Geometry.- Sharply 3-Transitivc Groups.- Mathieu Groups.- Steiner Systems.- 10 Abelian Groups.- Basics.- Free Abelian Groups.- Finitely Generated Abelian Groups.- Divisible and Reduced Groups.- Torsion Groups.- Subgroups of ?.- Character Groups.- 11 Free Groups and Free Products.- Generators and Relations.- SemigroupInterlude.- Coset Enumeration.- Presentations and the Schur Multiplier.- Fundamental Groups of Complexes.- Tietze's Theorem.- Covering Complexes.- The Nielscn-Schreier Theorem.- Free Products.- The Kurosh Theorem.- The van Kampen Theorem.- Amalgams.- HNN Extensions.- 12 The Word Problem.- Turing Machines.- The MarkovPost Theorem.- The NovikovBooneBritton Theorem: Sufficiency of Boone's Lemma.- Cancellation Diagrams.- The NovikovBooneBritton Theorem: Necessity of Boone's Lemma.- The Higman Imbedding Theorem.- Some Applications.- Epilogue.- Appendix I Some Major Algebraic Systems.- Appendix II Equivalence Relations and Equivalence Classes.- Appendix III Functions.- APPENDIX IV Zorn's Lemma.- APPENDIX V Countability.- APPENDIX VI Commutative Rings.- Notation.Trade ReviewFourth Edition J.J. Rotman An Introduction to the Theory of Groups "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route."—MATHEMATICAL REVIEWSTable of Contents1 Groups and Homomorphisms.- Permutations.- Cycles.- Factorization into Disjoint Cycles.- Even and Odd Permutations.- Semigroups.- Groups.- Homomorphisms.- 2 The Isomorphism Theorems.- Subgroups.- Lagrange’s Theorem.- Cyclic Groups.- Normal Subgroups.- Quotient Groups.- The Isomorphism Theorems.- Correspondence Theorem.- Direct Products.- 3 Symmetric Groups and G-Sets.- Conjugates.- Symmetric Groups.- The Simplicity of An.- Some Representation Theorems.- G-Sets.- Counting Orbits.- Some Geometry.- 4 The Sylow Theorems.- p-Groups.- The Sylow Theorems.- Groups of Small Order.- 5 Normal Series.- Some Galois Theory.- The Jordan-Hölder Theorem.- Solvable Groups.- Two Theorems of P. Hall.- Central Series and Nilpotent Groups.- p-Groups.- 6 Finite Direct Products.- The Basis Theorem.- The Fundamental Theorem of Finite Abelian Groups.- Canonical Forms; Existence.- Canonical Forms; Uniqueness.- The Krull—Schmidt Theorem.- Operator Groups.- 7 Extensions and Cohomology.- The Extension Problem.- Automorphism Groups.- Semidirect Products.- Wreath Products.- Factor Sets.- Theorems of Schur-Zassenhaus and Gaschütz.- Transfer and Burnside’s Theorem.- Projective Representations and the Schur Multiplier.- Derivations.- 8 Some Simple Linear Groups.- Finite Fields.- The General Linear Group.- PSL(2, K).- PSL(m, K).- Classical Groups.- 9 Permutations and the Mathieu Groups.- Multiple Transitivity.- Primitive G-Sets.- Simplicity Criteria.- Affine Geometry.- Projective Geometry.- Sharply 3-Transitivc Groups.- Mathieu Groups.- Steiner Systems.- 10 Abelian Groups.- Basics.- Free Abelian Groups.- Finitely Generated Abelian Groups.- Divisible and Reduced Groups.- Torsion Groups.- Subgroups of ?.- Character Groups.- 11 Free Groups and Free Products.- Generators and Relations.- Semigroup Interlude.- Coset Enumeration.- Presentations and the Schur Multiplier.- Fundamental Groups of Complexes.- Tietze’s Theorem.- Covering Complexes.- The Nielscn-Schreier Theorem.- Free Products.- The Kurosh Theorem.- The van Kampen Theorem.- Amalgams.- HNN Extensions.- 12 The Word Problem.- Turing Machines.- The Markov—Post Theorem.- The Novikov—Boone—Britton Theorem: Sufficiency of Boone’s Lemma.- Cancellation Diagrams.- The Novikov—Boone—Britton Theorem: Necessity of Boone’s Lemma.- The Higman Imbedding Theorem.- Some Applications.- Epilogue.- Appendix I Some Major Algebraic Systems.- Appendix II Equivalence Relations and Equivalence Classes.- Appendix III Functions.- APPENDIX IV Zorn’s Lemma.- APPENDIX V Countability.- APPENDIX VI Commutative Rings.- Notation.
£68.40
Springer New York Coherent States Wavelets and Their Generalizations Theoretical and Mathematical Physics
Book SynopsisThis second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.).Table of ContentsCanonical Coherent States.- Positive Operator-Valued Measures and Frames.- Some Group Theory.- Hilbert Spaces.- Square Integrable and Holomorphic Kernels.- Covariant Coherent States.- Coherent States from Square Integrable Representations.- Some Examples and Generalizations.- CS of General Semidirect Product Groups.- CS of Product Groups.- CS Quantizations and Probabilistic Aspects.- Direct Wavelet Transforms.- Multidimensional Wavelets.- Wavelets Related to Other G Groups.- The Discretization Problem - Frames Sampling and All That.
£127.49
Birkhauser Boston The Theory of Jacobi Forms 55 Progress in Mathematics
£116.99
Springer New York Linear Representations of Finite Groups Graduate Texts in Mathematics 42
Book SynopsisThis book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.Trade ReviewFrom the reviews: "Serre’s book gives a fine introduction to representations for various audiences . . . As always with Serre, the exposition is clear and elegant, and the exercises contain a great deal of valuable information that is otherwise hard to find . . . it is highly recommended for specialists and nonspecialists alike." (Bulletin Of The American Mathematical Society)Table of ContentsPart I: Representations and Characters; 1. Generalities on Linear Representation; 2. Character Theory; 3. Subgroups, products, induced representations; 4. Compact Groups; 5. Examples; Bibliography Part I; Part II: Representation in Characteristic Zero; 6. The Group Algebra; 7. Induced Representations- Mackey's Criterion; 8. Examples of Induced Representations; 9. Artin's Theorem; 10. A Theorem of Brauer; 11. Applications of Brauer's Theorem; 12. Rationality Questions; 13. Rationality Questions: Examples; Bibliography Part II; Part III: Introduction to Brauer Theory; 14. The Groups Rk(G), Rk(G) and Pk(G); 15. The cde Triangle; 16. Theorems; 17. Proofs; 18. Modular Characters; 19. Application to Artin Representations; Appendix; Bibliography part III; Index of Notation; Index of Terminology.
£50.99
Springer London Ltd The Finite Simple Groups
Book SynopsisThisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].Trade ReviewFrom the reviews: “The book under review has as its main goal to give an introductory overview of the construction and main properties of all finite simple groups. … This book is the first one that attempts to give a systematic treatment of all finite simple groups, using the more recent and efficient constructions … . The author succeeds in making this important but difficult area of mathematics readily accessible to a large sector of the mathematical community, and for this we should be grateful.” (Felipe Zaldivar, The Mathematical Association of America, March, 2010)“One of the great achievements of mathematics was the classification of the finite simple groups … . the book brings much information to the classroom. It contains exactly those things one would like to know if one were to meet the individual simple groups for the first time. … perfectly suitable for an advanced course or seminar. … accessible also to those who are not great experts in group theory. Anyone interested in finite groups … should have this book on his or her bookshelf.” (Gernot Stroth, Mathematical Reviews, Issue 2011 e)“The author of this book has succeeded in giving an overview of all non-abelian finite simple groups which is accessible to non-experts. … For anyone who wants to get information on finite simple groups without having to tackle massive monographs this volume will be most welcome.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 164 (3), November, 2011)“It is the first text at this level in which all the finite simple groups are treated together, pointing out their connections. … The text is very well organised. The introduction, which forms the first chapter, contains a brief history and the statement of the classification theorem, together with sections giving remarks on the applications and the proof of the theorem. … Consequently the book may also be useful to a reader who just wants an introduction to a particular group or family of groups.” (Peter Shiu, The Mathematical Gazette, Vol. 95 (532), March, 2011)“This book is a unique introductory overview of all the finite simple groups, and thus it is suitable not only for specialists who are interested in finite simple groups but also for advanced undergraduate and graduate students in algebra. The section entitled ‘Further reading’ at the end of each chapter is a nice guide to further study of the subjects.” (Hiromichi Yamada, Zentralblatt MATH, Vol. 1203, 2011)Table of ContentsThe alternating groups.- The classical groups.- The exceptional groups.- The sporadic groups.
£29.99
Bento Books, Inc. Math Girls 5: Galois Theory
£18.52
Springer Nature Switzerland AG Complex Semisimple Quantum Groups and
Book SynopsisThis book provides a thorough introduction to the theory of complex semisimple quantum groups, that is, Drinfeld doubles of q-deformations of compact semisimple Lie groups. The presentation is comprehensive, beginning with background information on Hopf algebras, and ending with the classification of admissible representations of the q-deformation of a complex semisimple Lie group. The main components are: - a thorough introduction to quantized universal enveloping algebras over general base fields and generic deformation parameters, including finite dimensional representation theory, the Poincaré-Birkhoff-Witt Theorem, the locally finite part, and the Harish-Chandra homomorphism, - the analytic theory of quantized complex semisimple Lie groups in terms of quantized algebras of functions and their duals, - algebraic representation theory in terms of category O, and - analytic representation theory of quantized complex semisimple groups. Given its scope, the book will be a valuable resource for both graduate students and researchers in the area of quantum groups.Trade Review“The book is largely self-contained. … It is highly recommended for mathematicians of all levels wishing to learn about these topics, in the algebraic setting and/or in the analytic setting.” (Huafeng Zhang, zbMATH 1514.20006, 2023)Table of Contents- Introduction. - Multiplier Hopf Algebras. - Quantized Universal Enveloping Algebras. - Complex Semisimple Quantum Groups. - Category O. - Representation Theory of Complex Semisimple Quantum Groups.
£49.99
Springer Nature Switzerland AG A First Course in the Sporadic SICs
Book SynopsisThis book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty.While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.Table of ContentsEquiangular Lines.- Sporadic SICs and the Exceptional Lie Algebras.- The Hoggar-type SICs.-SICs as Equicoherent Quantum States.- SICs and Bell Inequalities.
£54.99
Springer Nature Switzerland AG Topics in Groups and Geometry: Growth,
Book SynopsisThis book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today.The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.Table of Contents- Foreword.- Preface.- Part I Algebraic Theory: 1. Free Groups.- 2. Nilpotent Groups.- 3. Residual Finiteness and the Zassenhaus Filtration.- 4. Solvable Groups.- 5. Polycyclic Groups.- 6. The Burnside Problem.- Part II Geometric Theory: 7. Finitely Generated Groups and Their Growth Functions.- 8. Hyperbolic Plane Geometry and the Tits Alternative.- 9. Topological Groups, Lie Groups, and Hilbert Fifth Problem.- 10. Dimension Theory.- 11. Ultrafilters, Ultraproducts, Ultrapowers, and Asymptotic Cones.- 12. Gromov’s Theorem.- Part III Analytic and Probabilistic Theory: 13. The Theorems of Polya and Varopoulos.- 14. Amenability, Isoperimetric Profile, and Følner Functions.- 15. Solutions or Hints to Selected Exercises.- References.- Subject Index.- Index of Authors.
£71.24
Springer Nature Switzerland AG Geometric Transformations
Book SynopsisThis textbook teaches the transformations of plane Euclidean geometry through problems, offering a transformation-based perspective on problems that have appeared in recent years at mathematics competitions around the globe, as well as on some classical examples and theorems. It is based on the combined teaching experience of the authors (coaches of several Mathematical Olympiad teams in Brazil, Romania and the USA) and presents comprehensive theoretical discussions of isometries, homotheties and spiral similarities, and inversions, all illustrated by examples and followed by myriad problems left for the reader to solve. These problems were carefully selected and arranged to introduce students to the topics by gradually moving from basic to expert level. Most of them have appeared in competitions such as Mathematical Olympiads or in mathematical journals aimed at an audience interested in mathematics competitions, while some are fundamental facts of mathematics discussed in the framework of geometric transformations. The book offers a global view of the geometric content of today's mathematics competitions, bringing many new methods and ideas to the attention of the public.Talented high school and middle school students seeking to improve their problem-solving skills can benefit from this book, as well as high school and college instructors who want to add nonstandard questions to their courses. People who enjoy solving elementary math problems as a hobby will also enjoy this work.Trade Review“This book … is a nice addition to the literature. … for instructors teaching geometry courses in which these are a topic, this book should provide an excellent source of interesting examples and problems. The large number of solved problems should also make useful reading for people preparing for mathematical contests and Olympiads.” (Mark Hunacek, MAA Reviews, October 4, 2022)Table of ContentsIntroduction.- Part I: Problems - 1. Isometries.- 2. Homotheties and Spiral Similarities.- 3. Inversions.- 4. A Synthesis.- Part II: Hints - 5. Isometries.- 6. Homotheties and Spiral Similarities.- 7. Inversions.- 8. A Synthesis.- Part III: Solutions - 9. Isometries.- 10. Homotheties and Spiral Similarities.- 11. Inversions.- 12. A Synthesis.
£54.99
Springer Nature Switzerland AG An Invitation to Representation Theory: Polynomial Representations of the Symmetric Group
Book SynopsisAn Invitation to Representation Theory offers an introduction to groups and their representations, suitable for undergraduates. In this book, the ubiquitous symmetric group and its natural action on polynomials are used as a gateway to representation theory.The subject of representation theory is one of the most connected in mathematics, with applications to group theory, geometry, number theory and combinatorics, as well as physics and chemistry. It can however be daunting for beginners and inaccessible to undergraduates. The symmetric group and its natural action on polynomial spaces provide a rich yet accessible model to study, serving as a prototype for other groups and their representations. This book uses this key example to motivate the subject, developing the notions of groups and group representations concurrently.With prerequisites limited to a solid grounding in linear algebra, this book can serve as a first introduction to representation theory at the undergraduate level, for instance in a topics class or a reading course. A substantial amount of content is presented in over 250 exercises with complete solutions, making it well-suited for guided study.Trade Review“The book under review is a nice introduction to the representation theory of the symmetric group. … The book is well structured and enriched with numerous exercises, many of which are solved or with hints for the solution.” (Enrico Jabara, zbMATH 1514.20002, 2023)Table of Contents Preface Introduction Chapter 1. First Steps Chapter 2. Polynomials, Subspaces, and Subrepresentations Chapter 3. Intertwining Maps, Complete Reducibility, and Invariant Inner Products Chapter 4. The Structure of the Symmetric Group Chapter 5. Sn Decomposition of Polynomial Spaces for n= 1,2,3. Chapter 6. The Group Algebra Chapter 7. The Irreducible Representations of Sn: Characters Chapter 8. The Irreducible Representations of Sn: Young Symmetrizers Chapter 9. Cosets, Restricted and Induced Representations Chapter 10. Direct Products of Groups, Young Subgroups and Permutation Modules Chapter 11. Specht Modules Chapter 12. Decomposition of Young Permutation Modules Chapter 13. Branching Relations Bibliography Index
£22.49
Springer Finite Groups I
Book Synopsis1 Foundations.- 2 Permutation groups and linear groups.- 3 Nilpotent groups and p-groups.- 4 Transfer and p-nilpotent groups.- 5 Representation theory.- 6 Solvable groups.
£183.35
Birkhauser Verlag AG Subgroup Growth
Book SynopsisAward-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged.As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.Trade ReviewSubgroup Growth is an extremely well-written book and is a delight to read. It has a wealth of information making a rich and timely contribution to an emerging area in the theory of groups which has come to be known as Asymptotic Group Theory. This monograph and the challenging open problems with which it concludes are bound to play a fundamental role in the development of the subject for many years to come. —Journal Indian Inst of Science "[Subgroup growth] is one of the first books on Asymptotic Group Theory – a new, quickly developing direction in modern mathematics…The book of A. Lubotzky and D.Segal, leading specialists in group theory, answers…questions in a beautiful way .…It was natural to expect a text on the subject that would summarize the achievements in the field and we are very lucky to witness the appearance of this wonderful book. …Readers will be impressed with the encyclopedic scope of the text. It includes all, or almost all, topics related to subgroup growth ….The book also includes plenty of general information on topics that are well known to algebraic audiences and should be part of the background for every modern researcher in mathematics. …a wonderful methodological tool introduced by the authors. … The book ends [with] a section on open problems, which contains 35 problems related to subgroup growth. The list will be useful and interesting to both established mathematicians and young researchers. There is no doubt that the list includes the most important and illuminating problems in the area, and we eagerly anticipate solutions of at least some of them in the near future. The book will surely have [a] big impact on all readers interested in Group Theory, as well as in Algebra and Number Theory in general." —Bulletin of the AMS "The proofs in this book employ a remarkable variety of tools, from all branches of group theory, certainly, but also from number theory, logic, and analysis…. The authors supply surveys, and some proofs, of necessary results, in the "windows" at the end of the book. These comprise about one quarter of the full book, and they give the needy reader a handy reference, without interrupting the flow of argument in the main text…. Since the subject of this book is an active area of current research, there are many open problems in it…." —Mathematical ReviewsTable of Contents0 Introduction and Overview.- 0.1 Preliminary comments and definitions.- 0.2 Overview of the chapters.- 0.3 On CFSG.- 0.4 The windows.- 0.5 The ‘notes’.- 1 Basic Techniques of Subgroup Counting.- 1.1 Permutation representations.- 1.2 Quotients and subgroups.- 1.3 Group extensions.- 1.4 Nilpotent and soluble groups.- 1.5 Abelian groups I.- 1.6 Finite p-groups.- 1.7 Sylow’s theorem.- 1.8 Rest riet ing to soluble subgroups.- 1.9 Applications of the ‘minimal index’.- 1.10 Abelian groups II.- 1.11 Growth types.- Notes.- 2 Free Groups.- 2.1 The subgroup growth of free groups.- 2.2 Subnormal subgroups.- 2.3 Counting d-generator finite groups.- Notes.- 3 Groups with Exponential Subgroup Growth.- 3.1 Upper bounds.- 3.2 Lower bounds.- 3.3 Free pro-p groups.- 3.4 Normal subgroups in free pro-p groups.- 3.5 Relations in p-groups and Lie algebras.- Notes.- 4 Pro-p Groups.- 4.1 Pro-p groups with polynomial subgroup growth.- 4.2 Pro-p groups with slow subgroup growth.- 4.3 The groups $$SL_r^1({\mathbb{F}_p}[[t]])$$.- 4.4 A-perfect groups.- 4.5 The Nottingham group.- 4.6 Finitely presented pro-p groups.- Notes.- 5 Finitely Generated Groups with Polynomial Subgroup Growth.- 5.1 Preliminary observations.- 5.2 Linear groups with PSG.- 5.3 Upper chief factors.- 5.4 Groups of prosoluble type.- 5.5 Groups of finite upper rank.- 5.6 The degree of polynomial subgroup growth.- Notes.- 6 Congruence Subgroups.- 6.1 The characteristic 0 case.- 6.2 The positive characteristic case.- 6.3 Perfect Lie algebras.- 6.4 Normal congruence subgroups.- Notes.- 7 The Generalized Congruence Subgroup Problem.- 7.1 The congruence subgroup problem.- 7.2 Subgroup growth of lattices.- 7.3 Counting hyperbolic manifolds.- Notes.- 8 Linear Groups.- 8.1 Subgroup growth, characteristic 0.- 8.2 Residually nilpotent groups.- 8.3 Subgroup growth, characteristic p.- 8.4 Normal subgroup growth.- Notes.- 9 Soluble Groups.- 9.1 Metabelian groups.- 9.2 Residually nilpotent groups.- 9.3 Some finitely presented metabelian groups.- 9.4 Normal subgroup growth in metabelian groups.- Notes.- 10 Profinite Groups with Polynomial Subgroup Growth.- 10.1 Upper rank.- 10.2 Profinite groups with wPSG: structure.- 10.3 Quasi-semisimple groups.- 10.4 Profinite groups with wPSG: characterization.- 10.5 Weak PSG = PSG.- Notes.- 11 Probabilistic Methods.- 11.1 The probability measure.- 11.2 Generation probabilities.- 11.3 Maximal subgroups.- 11.4 Further applications.- 11.5 Pro-p groups.- Notes.- 12 Other Growth Conditions.- 12.1 Rank and bounded generation.- 12.2 Adelic groups.- 12.3 The structure of finite linear groups.- 12.4 Composition factors.- 12.5 BG, PIG and subgroup growth.- 12.6 Residually nilpotent groups.- 12.7 Arithmetic groups and the CSP.- 12.8 Examples.- Notes.- 13 The Growth Spectrum.- 13.1 Products of alternating groups.- 13.2 Some finitely generated permutation groups.- 13.3 Some profinite groups with restricted composition factors.- 13.4 Automorphisms of rooted trees.- Notes.- 14 Explicit Formulas and Asymptotics.- 14.1 Free groups and the modular group.- 14.2 Free products of finite groups.- 14.3 Modular subgroup arithmetic.- 14.4 Surface groups.- Notes.- 15 Zeta Functions I: Nilpotent Groups.- 15.1 Local zeta functions as p-adic integrals.- 15.2 Alternative methods.- 15.3 The zeta function of a nilpotent group.- Notes.- 16 Zeta Functions II: p-adic Analytic Groups.- 16.1 Integration on pro-p groups.- 16.2 Counting subgroups in a p-adic analytic group.- 16.3 Counting orbits.- 16.4 Counting p-groups.- Notes.- Windows.- 1 Finite Group Theory.- 1 Hall subgroups and Sylow bases.- 2 Carter subgroups.- 3 The Fitting subgroup.- 4 The generalized Fitting subgroup.- 5 Tate’s theorem.- 6 Rank and p-rank.- 7 Schur multiplier.- 8 Powerful p-groups.- 9 GLn and Sym(n).- 2 Finite Simple Groups.- 1 The list.- 2 Generators.- 3 Subgroups.- 4 Representations.- 5 Automorphisms.- 6 Schur multipliers.- 7 An elementary proof.- 3 Permutation Groups.- 1 Primitive groups.- 2 Groups with restricted sections.- 3 Subgroups of alternating groups.- 4 Profinite Groups.- 1 Completions.- 2 Free profinite groups.- 3 Profinite presentations.- 5 Pro-p Groups.- 1 Generators and relations.- 2 Pro-p groups of finite rank.- 3 Linear pro-p groups over local fields.- 4 Automorphisms of finite p-groups.- 5 Hall’s enumeration principle.- 6 Soluble Groups.- 1 Nilpotent groups.- 2 Soluble groups of finite rank.- 3 Finitely generated metabelian groups.- 7 Linear Groups.- 1 Soluble groups.- 2 Jordan’s theorem.- 3 Monomial groups.- 4 Finitely generated groups.- 5 Lang’s theorem.- 8 Linearity Conditions for Infinite Groups.- 1 Variations on Mal’cev’s local theorem.- 2 Groups that are residually of bounded rank.- 3 Applications of Ado’s theorem.- 9 Strong Approximation for Linear Groups.- 1 A variant of the Strong Approximation Theorem.- 2 Subgroups of SLn(Fp).- 3 The ‘Lubotzky alternative’.- 4 Strong approximation in positive characteristic.- 10 Primes.- 1 The Prime Number Theorem.- 2 Arithmetic progressions and the Bombieri-Vinogradov theorem.- 3 Global fields and Chebotarev’s theorem.- 11 Probability.- 12 p-adic Integrals and Logic.- 1 Results.- 2 A peek inside the black box.- Open Problems.- 1 ‘Growth spectrum’.- 2 Normal subgroup growth in pro-p groups and metabelian groups.- 3 The degree of f.g. nilpotent groups.- 4 Finite extensions.- 5 Soluble groups.- 6 Isospectral groups.- 7 Congruence subgroups, lattices in Lie groups.- 8 Other growth conditions.- 9 Zeta functions.
£44.99
De Gruyter Finite Soluble Groups
Book SynopsisThe aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Aix-Marseille Université, France Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
£220.40
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Automorphic Forms on Semisimple Lie Groups
Table of ContentsI.- II.- III.- IV.- V.
£22.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG A Groupoid Approach to C*-Algebras
Table of ContentsLocally compact groupoids.- The C*-algebra of a groupoid.- Some examples.
£24.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Representations of Compact Lie Groups
Book SynopsisThis introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.Table of ContentsI Lie Groups and Lie Algebras.- II Elementary Representation Theory.- III Representative Functions.- IV The Maximal Torus of a Compact Lie Group.- V Root Systems.- VI Irreducible Characters and Weights.- Symbol Index.
£47.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Lie Groups
Book SynopsisThis (post) graduate text gives a broad introduction to Lie groups and algebras with an emphasis on differential geometrical methods. It analyzes the structure of compact Lie groups in terms of the action of the group on itself by conjugation, culminating in the classification of the representations of compact Lie groups and their realization as sections of holomorphic line bundles over flag manifolds. Appendices provide background reviews.Trade ReviewFrom the reviews: "This one is worth to read and to keep on your shelf! It presents the theory of Lie groups not only in the usual way of Lie algebraic treatment, but also from the global point of view. … Every chapter ends with very useful notes on the origins and connections of the chapter’s subject. References are given separately in each chapter. ... It is highly recommended to advanced undergraduate and graduated students in mathematics and physics." (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 75, 2009)Table of ContentsPreface 1 Lie Groups and Lie Algebras 1.1 Lie Groups and their Lie Algebras 1.2 Examples 1.3 The Exponential Map 1.4 The Exponential Map for a Vector Space 1.5 The Tangent Map of Exp 1.6 The Product in Logarithmic Coordinates 1.7 Dynkin's Formula 1.8 Lie's Fundamental Theorems 1.9 The Component of the Identity 1.10 Lie Subgroups and Homomorphisms 1.11 Quotients 1.12 Connected Commutative Lie Groups 1.13 Simply Connected Lie Groups 1.14 Lie's Third Fundamental Theorem in Global Form 1.15 Exercises 1.16 Notes References for Chapter One 2 Proper Actions 2.1 Review 2.2 Bochner's Linearization Theorem 2.3 Slices 2.4 Associated Fiber Bundles 2.5 Smooth Functions on the Orbit Space 2.6 Orbit Types and Local Action Types 2.7 The Stratification by Orbit Types 2.8 Principal and Regular Orbits 2.9 Blowing Up 2.10 Exercises 2.11 Notes References for Chapter Two 3 Compact Lie Groups 3.0 Introduction 3.1 Centralizers 3.2 The Adjoint Action 3.3 Connectedness of Centralizers 3.4 The Group of Rotations and its Covering Group 3.5 Roots and Root Spaces 3.6 Compact Lie Algebras 3.7 Maximal Tori 3.8 Orbit Structure in the Lie Algebra 3.9 The Fundamental Group 3.10 The Weyl Group as a Reflection Group 3.11 The Stiefel Diagram 3.12 Unitary Groups 3.13 Integration 3.14 The Weyl Integration Theorem 3.15 Nonconnected Groups 3.16 Exercises 3.17 Notes References for Chapter Three 4 Representations of Compact Groups 4.0 Introduction 4.1 Schur's Lemma 4.2 Averaging 4.3 Matrix Coefficients and Characters 4.4 G-types 4.5 Finite Groups 4.6 The Peter-Weyl Theorem 4.7 Induced Representations 4.8 Reality 4.9 Weyl's Character Formula 4.10 Weight Exercises 4.11 Highest Weight Vectors 4.12 The Borel-Weil Theorem 4.13 The Nonconnected Case 4.14 Exercises 4.15 Notes References for Chapter Four Appendix A Appendix B Appendix
£54.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algebraic Integrability, Painlevé Geometry and Lie Algebras
Book SynopsisIn the early 70's and 80's the field of integrable systems was in its prime youth: results and ideas were mushrooming all over the world. It was during the roaring 70's and 80's that a first version of the book was born, based on our research and on lectures which each of us had given. We owe many ideas to our colleagues Teruhisa Matsusaka and David Mumford, and to our inspiring graduate students (Constantin Bechlivanidis, Luc Haine, Ahmed Lesfari, Andrew McDaniel, Luis Piovan and Pol Vanhaecke). As it stood, our first version lacked rigor and precision, was rough, dis- connected and incomplete...In the early 90's new problems appeared on the horizon and the project came to a complete standstill, ultimately con- fined to a floppy. A few years ago, under the impulse of Pol Vanhaecke, the project was revived and gained real momentum due to his insight, vision and determination. The leap from the old to the new version is gigantic. The book is designed as a teaching textbook and is aimed at a wide read- ership of mathematicians and physicists, graduate students and professionals.Trade ReviewFrom the reviews of the first edition: "The aim of this book is to explain ‘how algebraic geometry, Lie theory and Painlevé analysis can be used to explicitly solve integrable differential equations’. … One of the main advantages of this book is that the authors … succeeded to present the material in a self-contained manner with numerous examples. As a result it can be also used as a reference book for many subjects in mathematics. In summary … a very good book which covers many interesting subjects in modern mathematical physics." (Vladimir Mangazeev, The Australian Mathematical Society Gazette, Vol. 33 (4), 2006) "This is an extensive volume devoted to the integrability of nonlinear Hamiltonian differential equations. The book is designed as a teaching textbook and aims at a wide readership of mathematicians and physicists, graduate students and professionals. … The book provides many useful tools and techniques in the field of completely integrable systems. It is a valuable source for graduate students and researchers who like to enter the integrability theory or to learn fascinating aspects of integrable geometry of nonlinear differential equations." (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1083, 2006)Table of Contents1 Introduction.- 2 Lie Algebras.- 3 Poisson Manifolds.- 4 Integrable Systems on Poisson Manifolds.- 5 The Geometry of Abelian Varieties.- 6 A.c.i. Systems.- 7 Weight Homogeneous A.c.i. Systems.- 8 Integrable Geodesic Flow on SO(4).- 9 Periodic Toda Lattices Associated to Cartan Matrices.- 10 Integrable Spinning Tops.- References.
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Groupes et algèbres de Lie: Chapitres 2 et 3
Book SynopsisCe deuxième volume du Livre sur les Groupes et algèbres de Lie, neuvième Livre du traité, comprend les chapitres: 2. Algèbres de Lie libres; 3. Groupes de Lie. Le chapitre 2 poursuit la présentation des notions fondamentales des algèbres de Lie avec l’introduction des algèbres de Lie libres et de la série de Hausdorff. Le chapitre 3 est consacré aux concepts de base pour les groupes de Lies sur un corps archimédien ou ultramétrique.Table of ContentsAlgèbres de Lie libres.- Groupes de Lie.
£54.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Groupes et algèbres de Lie: Chapitre 9 Groupes de
Book SynopsisLes Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce neuvième chapitre du Livre sur les Groupes et algèbres de Lie, neuvième Livre du traité, comprend les paragraphes: §1 Algèbres de Lie compactes; §2 Tores maximaux des groupes de Lie compacts; §3 Fromes compactes des algèbres de Lie semi-simples complexes; §4 Système de raciness associé à un groupe compact; §5 Classes de conjugaison; §6 Intégration dans les groupes de Lie compacts; §7 Représentations irréductibles des groupes de Lie compacts connexes; §8 Transformation de Fourier; §9 Opération des groupes de Lie compacts sur les variétés. Ce volume a été publié en 1982.Table of ContentsGroupes de Lie réels compacts.
£34.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Algèbre: Chapitre 8
Book SynopsisCe huitième chapitre du Livre d'Algèbre, deuxième Livre des Éléments de mathématique, est consacré à l'étude de certaines classes d'anneaux et des modules sur ces anneaux.Il couvre les notions de module et d'anneau noethérien et artinien, ainsi que celle de radical. Ce chapitre décrit également la structure des anneaux semi-simples. Nous y donnons aussi la définition de divers groupes de Grothendieck qui jouent un rôle universel pour les invariants de modules et plusieurs descriptions du groupe de Brauer qui intervient dans la classification des anneaux simples.Une note historique en fin de volume, reprise de l'édition précédente, retrace l'émergence d'une grande partie des notions développées.Ce volume est une deuxième édition entièrement refondue de l'édition de 1958.Trade ReviewFrom the reviews of the second edition:“This book is intended as a comprehensive exposition of the theory of semi-simple rings and modules, with special emphasis on the Noetherian and Artinian cases. … Each section ends with a large collection of related exercises in the typical Bourbaki-style … . Certainly, it has been both a splendid idea and a great undertaking to rewrite N. Bourbaki’s classic Chapter 8 of Book II of the ‘Elements of Mathematics’ in such excellent a manner, very much so to the benefit of further generations of mathematicians.” (Werner Kleinert, Zentralblatt MATH, Vol. 1245, 2012)Table of ContentsIntroduction.- Chapitre VIII. Modules et anneaux semi-simples.- 1. Modules artiniens et modules noethériens.- 2. Structure des modules de longueur finie.- 3. Modules simples.- 4. Modules semi-simples.- 5. Commutation.- 6. Équivalence de Morita des modules et des algèbres.- 7. Anneaux simples.- 8. Anneaux semi-simples.- 9. Radical.- 10. Modules sur un anneau artinien.- 11. Groupes de Grothendieck.- 12. Produit tensoriel de modules semi-simples.- 13. Algèbres absolument semi-simples.- 14. Algèbres centrales et simples.- 15. Groupes de Brauer.- 16. Autres descriptions du groupe de Brauer.- 17. Normes et traces réduites.- 18. Algèbres simples sur un corps fini.- 20. Représentations linéaires des algèbres.- 21. Représentations linéaires des groupes finis.- Appendice 1. Algèbres sans élément unité.- Appendice 2. Déterminants sur un corps non commutatif.- Appendice 3. Le théorème des zéros de Hilbert.- Appendice 4. Trace d’un endomorphisme de rang fini.- Note Historique.- Bibliographie.- Index des notations.- Index terminologique
£41.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Intégration: Chapitres 7 à 8
Book SynopsisCe volume du Livre d’Intégration, sixième Livre du traité, traite de l’intégration sur les groupes localement compacts et de ses applications. Les notions introduites, telles que les mesures de Haar et le produit de convolution, sont à la base de l’analyse harmonique. Il comprend les chapitres : -1. Mesure de Haar ; -2. Convolution et représentations.Table of ContentsMesure de Haar.- Convolution et Représentation.
£39.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Octonions, Jordan Algebras and Exceptional Groups
Book SynopsisThe 1963 Göttingen notes of T. A. Springer are well known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra. Trade ReviewFrom the reviews of the first edition: "This book is an updated and revised English version of the German notes on octaves, Jordan algebras and exceptional groups which appeared as mimeographed lecture notes of Göttingen University in 1963. It is still an excellent reference on the subject … ." (Huberta Lausch, Zentralblatt MATH, Vol. 1087, 2006)Table of Contents1. Composition Algebras.- 2. The Automorphism Group of an Octonion Algebra.- 3. Triality.- 4. Twisted Composition Algebras.- 5. J-algebras and Albert Algebras.- 6. Proper J-algebras and Twisted Composition Algebras.- 7. Exceptional Groups.- 8. Cohomological Invariants.
£94.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Lie Groups and Lie Algebras: Chapters 4-6
Book SynopsisFrom the reviews of the French edition: "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or ‘Tits systems’". --G.B. Seligman in MathReviews.Table of ContentsCoxeter Groups and Tits Systems.- Groups Generated by Reflections.- Root Systems.
£53.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Local Langlands Conjecture for GL(2)
Book SynopsisThe Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.Trade ReviewFrom the reviews:"In this book the authors present a complete proof of the Langlands conjecture for GL (2) over a non-archimedean local field, which uses local methods and is accessible to students. … The book is very well written and easy to read." (J. G. M. Mars, Zentralblatt MATH, Vol. 1100 (2), 2007)"The book under review gives a complete and self-contained insight into the theory of representations of G. … We highly recommend this book to Ph.D. students as well as to specialists. The book contains a huge amount of information, definition and facts … . The book has a Bibliography containing 91 references … ." (Alexandru Ioan Badulescu, Mathematical Reviews, Issue 2007 m)“The aim of this monograph is to present a complete and self-contained proof of the Langlands conjecture for GL(2) over a non-archimedean local field. … This volume presents a large amount of difficult material in a clear and readable manner. It can be recommended to anyone interested in representations of linear algebraic groups.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 154 (4), August, 2008)Table of ContentsSmooth Representations.- Finite Fields.- Induced Representations of Linear Groups.- Cuspidal Representations.- Parametrization of Tame Cuspidals.- Functional Equation.- Representations of Weil Groups.- The Langlands Correspondence.- The Weil Representation.- Arithmetic of Dyadic Fields.- Ordinary Representations.- The Dyadic Langlands Correspondence.- The Jacquet-Langlands Correspondence.
£132.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Group Theory: Application to the Physics of Condensed Matter
Book SynopsisThis concise, class-tested book was refined over the authors’ 30 years as instructors at MIT and the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory along with applications helps students to learn, understand and use it for their own needs. Thus, the theoretical background is confined to introductory chapters. Subsequent chapters develop new theory alongside applications so that students can retain new concepts, build on concepts already learned, and see interrelations between topics. Essential problem sets between chapters aid retention of new material and consolidate material learned in previous chapters.Trade ReviewFrom the reviews:"It was developed for a graduate course taught mostly by Millie Dresselhaus at MIT for more than 30 years, with many revisions of lecture notes. Very much a graduate text or specialist monograph, the book covers a wealth of applications across solid-state physics. … The book can be warmly recommended to students and researchers in solid-state physics, either to serve as a text for an advanced lecture course or for individual study … ." (Volker Heine, Physics Today, November, 2008)"This textbook is based on the authors’ pedagogical experience during their 30 years at MIT. … the book develops all of the relevant mathematics (linear algebra) and the necessary physics (quantum mechanics), it is eminently suitable to a wide audience in physics, chemistry and materials science." (Barry R. Masters, Optics and Photonics News, July/August, 2009)“This is an excellent text … . originates from lectures by Charles Kittel and J. H. van Vleck in the 1950s and much of the material was presented in courses by the authors over the last three decades. The material is meant for Electrical Engineering and Physics students at the graduate level … . has exercises at the end of each chapter and an extensive set of appendices. The exposition is clear and detailed. This is a very good book for its target audience.” (W. Miller Jr., Zentralblatt MATH, Vol. 1175, 2010)“The goal of the book under review is to teach group theory in close connection to applications. … Every chapter of the book finishes with several selected problems. Specific to this book is the feature that every abstract theoretical group concept is introduced and applied in a concrete physical way. This is why the book is very useful for anyone interested in applications of group theory to the wide range of condensed matter phenomena.” (Oktay K. Pashaev, Mathematical Reviews, Issue 2010 i)“It is highly welcomed because of its well-thought structuring and the plenty of non-trivial examples. The authors develop those parts of the theory of groups which are interesting for physicists, from chapter to chapter offering nearly at any step one or more informative application.” (G. Kowol, Monatshefte für Mathematik, Vol. 157 (2), June, 2009)Table of ContentsBasic Mathematics.- Basic Mathematical Background: Introduction.- Representation Theory and Basic Theorems.- Character of a Representation.- Basis Functions.- Introductory Application to Quantum Systems.- Splitting of Atomic Orbitals in a Crystal Potential.- Application to Selection Rules and Direct Products.- Molecular Systems.- Electronic States of Molecules and Directed Valence.- Molecular Vibrations, Infrared, and Raman Activity.- Application to Periodic Lattices.- Space Groups in Real Space.- Space Groups in Reciprocal Space and Representations.- Electron and Phonon Dispersion Relation.- Applications to Lattice Vibrations.- Electronic Energy Levels in a Cubic Crystals.- Energy Band Models Based on Symmetry.- Spin–Orbit Interaction in Solids and Double Groups.- Application of Double Groups to Energy Bands with Spin.- Other Symmetries.- Time Reversal Symmetry.- Permutation Groups and Many-Electron States.- Symmetry Properties of Tensors.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Clifford Algebras and Lie Theory
Book SynopsisThis monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem.This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra.Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.Table of ContentsPreface.- Conventions.- List of Symbols.- 1 Symmetric bilinear forms.- 2 Clifford algebras.- 3 The spin representation.- 4 Covariant and contravariant spinors.- 5 Enveloping algebras.- 6 Weil algebras.- 7 Quantum Weil algebras.- 8 Applications to reductive Lie algebras.- 9 D(g; k) as a geometric Dirac operator.- 10 The Hopf–Koszul–Samelson Theorem.- 11 The Clifford algebra of a reductive Lie algebra.- A Graded and filtered super spaces.- B Reductive Lie algebras.- C Background on Lie groups.- References.- Index.
£113.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Group Theory and Quantum Mechanics
Book SynopsisThe German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.Table of Contents1. Fundamental Notions of Quantum Mechanics.- § 1. Wave Functions.- § 2. Hilbert Spaces.- § 3. Linear Operators.- § 4. Hypermaximal Operators.- § 5. Separation of Variables.- § 6. One Electron in a Central Field.- § 7. Perturbation Theory.- § 8. Angular Momentum and Infinitesimal Rotations.- 2. Groups and Their Representations.- § 9. Linear Transformations.- § 10. Groups.- § 11. Equivalence and Reducibility of Representations.- § 12. Representations of Abelian Groups. Examples.- § 13. Uniqueness Theorems.- § 14. Kronecker’s Product Transformation.- § 15. The Operators Commuting with all Operators of a Given Representation.- § 16. Representations of Finite Groups.- § 17. Group Characters.- 3. Translations, Rotations and Lorentz Transformations.- § 18. Lie Groups and their Infinitesimal Transformations.- A. Lie Groups.- B. One-dimensional Lie Groups and Semi-Groups.- C. Causality and Translations in Time.- D. The Lie Algebra of a Lie Group.- E. Representations of Lie Groups.- § 19. The Unitary Groups SU(2) and the Rotation Group O3.- § 20. Representations of the Rotation Group O3.- § 21. Examples and Applications.- A. The Product Representation ?j × ?j’.- B. The Clebsch-Gordan Series.- C. Applications of (21.1).- D. The Reflection Character.- § 22. Selection and Intensity Rules.- § 23. The Representations of the Lorentz Group.- A. The Group SL(2) and the Restricted Lorentz Group.- B. Infinitesimal Transformations.- C. The Relation between World Vectors and Spinors.- IV. The Spinning Electron.- § 24. The Spin.- § 25. The Wave Function of the Spinning Electron.- A. Pauli’s Pair of Functions (?1, ?2).- B. Transformation of the Pair (?1, ?2).- C. Infinitesimal Rotations.- D. The Angular Momenta.- E. The Doublet Splitting of the Alkali Terms.- G. The Inversion s.- § 26. Dirac’s Wave Equation.- § 27. Two-Component Spinors.- A. Dirac’s Equation Rewritten.- B. Weyl’s Equation.- § 28. The Several Electron Problem. Multiplet Structure. Zeeman Effect.- V. The Group of Permutations and the Exclusion Principle.- § 29. The Resonance of Equal Particles.- § 30. The Exclusion Principle and the Periodical System.- § 31. The Eigenfunctions of the Atom.- § 32. The Calculation of the Energy Values.- § 33. Pure Spin Functions and their Transformation under Rotations and Permutations.- § 34. Representations of the Symmetric Group Sn.- VI. Molecule Spectra.- § 35. The Quantum Numbers of the Molecule.- § 36. The Rotation Levels.- § 37. The Case of Two Equal Nuclei.- Author and Subject Index.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Einhüllende Algebren halbeinfacher Lie-Algebren
Table of Contents1. Einhüllende Algebren.- 2. Halbeinfache Lie-Algebren.- 3. Zentralisatoren in Einhüllenden halbeinfacher Lie-Algebren.- 4. Moduln mit einem höchsten Gewicht.- 5. Annullatoren einfacher Moduln mit einem höchsten Gewicht.- 6. Harish-Chandra-Moduln.- 7. Primitive Ideale und Harish-Chandra-Moduln.- 8. Gel’fand-Kirillov-Dimension und Multiplizität.- 9. Die Multiplizität von Moduln in der Kategorie O.- 10. Gel’fand-Kirillov-Dimension von Harish-Chandra-Moduln.- 11. Lokalisierungen von Harish-Chandra-Moduln.- 12. Goldie-Rang und Kostants Problem.- 13. Schiefpolynomringe und der Übergang zu den m-Invarianten.- 14. Goldie-Rang-Polynome und Darstellungen der Weylgruppe.- 15. Induzierte Ideale und eine Vermutung von Gel’fand und Kirillov.- 16. Kazhdan-Lusztig-Polynome und spezielle Darstellungen der Weylgruppe.- 17. Assoziierte Varietäten.- Literatur.- Verzeichnis der Notationen.
£46.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Quantum Groups and Their Primitive Ideals
Book Synopsisby a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature.Table of ContentsI. Hopf Algebras.- 1.1 Axioms of a Hopf Algebra.- 1.2 Group Algebras and Enveloping Algebras.- 1.3 Adjoint Action.- 1.4 The Hopf Dual.- 1.5 Comments and Complements.- 2. Excerpts from the Classical Theory.- 2.1 Lie Algebras.- 2.2 Algebraic Lie Algebras.- 2.3 Algebraic Groups.- 2.4 Lie Algebras of Algebraic Groups.- 2.5 Comments and Complements.- 3. Encoding the Cartan Matrix.- 3.1 Quantum Weyl Algebras.- 3.2 The Drinfeld Double.- 3.3 The Rosso Form and the Casimir Invariant.- 3.4 The Classical Limit and the Shapovalev Form.- 3.5 Comments and Complements.- 4. Highest Weight Modules.- 4.1 The Jantzen Filtration and Sum Formula.- 4.2 Kac-Moody Lie Algebras.- 4.3 Integrable Modules for Uq(gc).- 4.4 Demazure Modules and Product Formulae.- 4.5 Comments and Complements.- 5. The Crystal Basis.- 5.1 Operators in the Crystal Limit.- 5.2 Crystals.- 5.3 Ad-invariant Filtrations, Twisted Actions and the Crystal Basis for Uq(n-).- 5.4 The Grand Loop.- 5.5 Comments and Complements.- 6. The Global Bases.- 6.1 The ? Operation and the Embedding Theorem.- 6.2 Globalization.- 6.3 The Demazure Property.- 6.4 Littelmann’s Path Crystals.- 6.5 Comments and Complements.- 7. Structure Theorems for Uq(g).- 7.1 Local Finiteness for the Adjoint Action.- 7.2 Positivity of the Rosso Form.- 7.3 The Separation Theorem.- 7.4 Noetherianity.- 7.5 Comments and Complements.- 8. The Primitive Spectrum of Uq(g).- 8.1 The Poincaré Series of the Harmonic Space.- 8.2 Factorization of the Quantum PRV Determinants.- 8.3 Verma Module Annihilators.- 8.4 Equivalence of Categories.- 8.5 Comments and Complements.- 9. Structure Theorems for Rq[G].- 9.1 Commutativity Relations.- 9.2 Surjectivity and Injectivity Theorems.- 9.3 The Adjoint Action.- 9.4 The R-Matrix.- 9.5 Comments and Complements.- 10. The Prime Spectrum of Rq[G].- 10.1 Highest Weight Modules.- 10.2 The Quantum Weyl Group.- 10.3 Prime and Primitive Ideals of Rq[G].- 10.4 Hopf Algebra Automorphisms.- 10.5 Comments and Complements.- A.2 Excerpts from Ring Theory.- A.3 Combinatorial Identities and Dimension Theory.- A.4 Remarks on Constructions of Quantum Groups.- A.5 Comments and Complements.- Index of Notation.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Topologie algébrique: Chapitres 1 à 4
Book SynopsisCe livre des Éléments de mathématique est consacré à la Topologie algébrique. Les quatre premiers chapitres présentent la théorie des revêtements d'un espace topologique et du groupe de Poincaré. On construit le revêtement universel d'un espace connexe pointé délaçable et on établit l'équivalence de catégories entre revêtements de cet espace et actions du groupe de Poincaré. On démontre une version générale du théorème de van Kampen exprimant le groupoïde de Poincaré d'un espace topologique comme un coégalisateur de diagrammes de groupoïdes. Dans de nombreuses situations géométriques, on en déduit une présentation explicite du groupe de Poincaré.Table of ContentsMode d'Emploi.- Introduction.- Chapitre I. Revêtements.- 1. Produits fibrés et carrés cartésiens.- 2. Applications étales.- 3. Faisceaux.- 4. Revêtements.- 5. Revêtements principaux.- 6. Espaces simplement connexes.- Exercices.- Chapitre II. Groupoïdes.- 1. Carquois.- 2. Graphes.- 3. Groupoïdes.- 4. Homotopies.- 5. Coégalisateur.- Exercices.- Chapitre III. Homotopie et Groupoïdes de Poincaré.- 1. Homotopies, homéotopies.- 2. Homotopie et chemins.- 3. Groupoïde de Poincaré.- 4. Homotopie et revêtements.- 5. Homotopie et revêtements (cas des espaces localement connexes par arcs).- Exercices.- Chapitre IV. Espaces Delaçables.- 1. Espaces délaçables.- 2. Groupes de Poincaré des espaces délaçables.- 3. Groupes de Poincaré des groupes topologiques.- 4. Théorie de la descente.- 5. Théorème de van Kampen.- 6. Espaces classifiants.- Exercices.- Index des notations.- Index terminologique.
£29.99
Springer Spektrum Übungsbuch zur Darstellungstheorie der endlichen
Book SynopsisVowort.- 1 Übungsaufgaben.- 2 Lösungen.- Literatur.- Index.
£999.99
Birkhäuser Symmetry in Geometry and Analysis Volume 3
Book SynopsisA solution to Duflo's polynomial problem for nilpotent Lie groups restricted representations (Ali Baklouti and Hidenori Fujiwara).- Multiplicities and associated varieties in representation theory of reductive groups (Dmitry Gourevitch).-Kobayashi's Conjectures on the Discrete Decomposability (Masatoshi Kitagawa).- Kobayashi's multiplicity-one theorems in branching laws and orbit philosophy beyond tempered representations (Salma Nasrin).- Discrete branching laws of derived functor modules (Yoshiki Oshima).- Rankin-Cohen brackets for orthogonal Lie algebras and bilinear conformally equivariant differential operators (Petr Somberg).
£999.99
James Clarke & Co Ltd Handbook of Cubik Math
Book SynopsisA clear explanation of the mathematics that underlies comprehension of Rubik's Cube, and how the cube itself can be used to grasp the fundamentals of group theory.Trade Review"The best book yet written - or likely to be written - on the wonders and the dark, unsolved mysteries of the cube" Martin Gardiner "Frey and Singmaster give a nicely blended discussion of specific algorithms for the cube together with some underlying theoretical concepts from group theory. Thus, cubists will be able to cure their insomnia by reading Chapter 3, and then perhaps satisfy their aroused curiosity about what is really going on by reading further" David M. Goldschmidt, Professor of Mathematics, University of California, Berkeley "Frey and Singmaster masterfully use the Rubik's cube to give a very tangible and tactile feel to the abstract concept of a group ... the book remains the definitive source for cube mathematics and presents an interesting and accessible introduction to group theory." David A. Reimann, in Mathematical Reviews, Issue 2012dTable of ContentsPreface 1. Introduction 2. A Cubik Orientation 3. Restoring the Cube 4. The What, Why, and How of Cube Movements 5. Improved Restoration Processes 6. The Cube Group and Subgroups 7. Permutation Structures and the Order of Groups 8. Advanced Restoration Methods 9. Epilogue A. A Small Catalogue of Processes B. Solutions to Exercises Index
£18.29
Taylor & Francis Inc Understanding Group Behavior Volume 1 Consensual
Book SynopsisThe second of two volumes addressing theoretical problems associated with consensual action of task-orientated small groups. Less formal than the first volume, this work tends to be more general in approach focusing on interpersonal relations and social processes within such groups.Trade Review"The field has long been preoccupied by certain topics--decision making, leadership, and performance--and the contents reflect that continuing emphasis. Witte and Davis have done the field a great service in bringing these papers together for publication."—Contemporary PsychologyTable of ContentsVolume 1.Contents: Preface. Part I: Introduction.J.H. Davis, Small-Group Research and the Steiner Questions: The Once and Future Thing. Part II: Social Aggregation and Combination Models.H.W. Crott, J. Werner, C. Hoffmann, A Probabilistic Model of Opinion Change Considering Distance Between Alternatives: An Application to Mock Jury Data. J.H. Davis, Group Decision Making and Quantitative Judgments: A Consensus Model. P.R. Laughlin, Group Decision Making and Collective Induction. R.S. Tindale, C.M. Smith, L.S. Thomas, J. Filkins, S. Sheffey, Shared Representations and Asymmetric Social Influence Processes in Small Groups. N.L. Kerr, R.J. MacCoun, G.P. Kramer, "When are N Heads Better (or Worse) Than One?": Biased Judgment in Individuals Versus Groups. T. Kameda, Procedural Influence in Consensus Formation: Evaluating Group Decision Making From a Social Choice Perspective. Part III: Social Information-Processing Models.G. Stasser, S.I. Vaughan, Models of Participation During Fact-to-Face Unstructured Discussion. B. Latané, Strength From Weakness: The Fate of Opinion Minorities in Spatially Distributed Groups. D. Gigone, R. Hastie, The Impact of Information on Group Judgment: A Model and Computer Simulation. E.H. Witte, The Extended Group Situation Theory (EGST): Explaining the Amount of Change. S. Galam, When Humans Interact Like Atoms. J.H. Davis, Concluding Remarks. Volume 2.Contents: Preface. Part I: Introduction.E.H. Witte, Small-Group Research and the Crisis of Social Psychology: An Introduction. Part IIGroup Structure and Composition.R.L. Moreland, J.M. Levine, M.L. Weingert, Creating the Ideal Group: Composition Effects at Work. W. Stroebe, M. Diehl, G. Abakoumkin, Social Compensation and the Köhler Effect: Toward a Theoretical Explanation of Motivation Gains in Group Productivity. H.A.M. Wilke, Status Congruence in Small Groups. J.C. Jesuino, Leadership: Micro-Macro Links. W. Scholl, Effective Teamwork -- A Theoretical Model and a Test in the Field. M. von Cranach, Toward a Theory of the Acting Group. Part III: Interpersonal Influence, Conflict, and Resolution.J.A. Pérez, G. Mugny, The Conflict Elaboration Theory of Social Influence. D. Frey, S. Schulz-Hardt, D. Stahlberg, Information Seeking Among Individuals and Groups and Possible Consequences for Decision Making in Business and Politics. M.A. Hogg, Social Identity, Self-Categorization, and the Small Group. J.M. Rabbie, H.F.M. Lodewijkx, A Behavioral Interaction Model: Toward an Integrative Theoretical Framework for Studying Intra- and Intergroup Dynamics. E.H. Witte, Similarities Among Various Conceptual Positions and Theoretical Points of View.
£80.74
Taylor & Francis Inc Time and Intimacy A New Science of Personal
Book SynopsisThere is a mysterious connection between our experiences of intimacy--of love, the longing to feel connected, and sexual embrace--and the human sense of time--eternity, impermanence, and rhythm. In this critical analysis of the time-intimacy equation, Bennett shows how the scientific study of personal relationships can address this mystery. As a study of transpersonal science, this book points to the possible evolution of intimacy and of our consciousness of time, and how the two evolutionary paths weave together. Dr. Bennett draws from a wide array of resources to advance and marry two compelling themes: first, the social and clinical science of personal relationships should integrate the spiritual or transpersonal dimension of intimacy, and second, science can contribute to lay understandings by describing the richly temporal aspects of relationships. In blending popular literature, transpersonal psychology, and scientific research and theory, this work also attempts to addrTrade Review"Joel Bennett's Time and Intimacy talks about intimacy in a way that recreates the feeling of intimacy, and recapitulates his vision of an intimate interaction through the structure of the book itself. Just as intimate interactions provide a sense of transcending time even as they can only be understood within a temporary trajectory, Bennett's prose, by refusing linearity and traditional scientific discourse, recapitulates the felt sense of an intimate interaction through its poetic style. Time and Intimacy is a book that can be opened anywhere and enjoyed, as it is composed of many loosely woven strands pulled together graphically and sometimes metaphorically. When it is opened spontaneously and absorbed in bursts, with full attention given to the language itself, it can be appreciated like poetry. Unlike poetry, however, Bennett's work has woven within it references to the latest research on close relationships. For readers who believe that the structure of the text should speak to the subject matter of that text, there is much experimentation with textual structure to be discovered in Time and Intimacy. Language alternates in unpredictable ways between the poetic and the philosophical, between the scientific and the transpersonal, between the objective and the subjective. Much as an intimate conversation itself might, the book invites the reader to transcend the ordinary boundaries of academic disciplines and to think about intimate experience in language that goes beyond ordinary discourse."—Karen PragerUniversity of Texas, Dallas"This book delves deeply and reveals to the reader a rich and new way to look at the realm of relationships. Simultaneously exploring time and intimacy creates a profound shift in our understanding of how people relate. In a modern era that views time as a commodity, intimacy is often lost as relationship suffers. Joel Bennett provides a brilliant approach to a very important subject--well worth any reader's time."—Stephan Rechtschaffen, MDAuthor, Time Shifting: Creating More Time to Enjoy Your Life; Cofounder and CEO,"Bennett has done an extraordinary job of combining three forms of reflection to treat the topic of intimacy. The integration of three themes--quantitative psychology research, transpersonal depth psychology, and temporality/transcendence--constitutes the unique contribution of this book. Time and Intimacy: A New Science of Personal Relationships presents a hypothesis for further reflection in psychology, and it organizes a whole field of research for study. Most important, it deals sensitively with a very important topic."—Robert Cummings NevilleDean, School of Theology, Boston UniversityTable of ContentsContents: S. Duck, Series Editor's Foreword. Preface. Introduction. Intimacy as a Journey Through This Text: Time and Change From Transcription to Transcendence. Unfolding in Time: Intimacy Across Situations. The Forces of Time: The Process of Intimacy. Time, Addiction, and Intimacy: Scripts, Archescripts, & Holoscripts. Temporal Context in Love and Science: The Weave of Temporal Sensitivity. In Search of the Temporal in Personal Relationship Research: From Temporal Initiative to Temporal Scale. Theories of Personal Relationships and the Contextual Model. Summary and Integration: Toward a Transpersonal Science. Appendix.
£128.25
Taylor & Francis Inc Maintaining Relationships Through Communication
Book SynopsisRelational maintenance provides a rallying point for those seeking to discover the behaviors that individuals utilize to sustain their personal relationships. Theoretical models, research programs, and specific studies have examined how people in a variety of close relationships choose to define and maintain those relationships. In addition, relational maintenance turns our attention to communicative processes that help people sustain their close relationships. In this collection, editors Daniel J. Canary and Marianne Dainton focus on the communicative processes critical to the maintenance and enhancement of personal relationships. The volume considers variations in maintaining different types of personal relationships; structural constraints on relationship maintenance; and cultural variations in relational maintenance. Contributions to the volume cover a broad range of relational types, including romantic relationships, family relationships, long-distance relationships, workplace relationships, and Gay and Lesbian relationships, among others. Maintaining Relationships Through Communication: Relational, Contextual, and Cultural Variations synthesizes current research in relationship maintenance, emphasizes the ways that behaviors vary in their maintenance functions across relational contexts, discusses alternative explanations for maintaining relationships, and presents avenues for future research. As such, it is intended for students and scholars studying interpersonal communication and personal relationships.Table of ContentsChapter 1 Definitions and Perspectives on Relational Maintenance Communication, Kathryn Dindia; Part 1 Maintaining Different Types of Relationships; Chapter 2 Maintaining Family Relationships, Sally Vogl-Bauer; Chapter 3 Maintaining Romantic Relationships: A Summary and Analysis of One Research Program, Laura Stafford; Chapter 4 Maintaining Friendships Throughout the Lifespan, Marianne Dainton, Elaine Zelley, Emily Langan; Chapter 5 Maintaining Undesired Relationships, Jon A. Hess; Part 2 Contextual Variations in Maintaining Relationships; Chapter 6 Maintaining Long-Distance Relationships, Brooks A. Aylor; Chapter 7 Computer-Mediated Communication Effects on Relationship Formation and Maintenance, Michael K. Rabby, Joseph B. Walther; Chapter 8 Relationship Maintenance in Organizational Settings, Vincent R. Waldron; Chapter 9 When Part ners Falter: Repair After a Transgression, Tara M. Emmers-Sommer; Part 3 Cultural Variations in Maintaining Relationships; Chapter 10 Relationship Maintenance in Same-Sex Couples, Stephen M. Haas; Chapter 11 Relationship Maintenance in Intercultural Couples: An Interdependence Analysis, Stanley O. Gaines, Jr., Christopher R. Agnew; Chapter 12 Maintaining Marriages in Russia: Managing Societal Influences and Communication Dynamics, Deborah S. Ballard-Reisch, Marat Zaguidoulline, Daniel J. Weigel; Chapter 13 Maintaining Relationships in Korea and the United States: Features of Korean Culture that Affect Relational Maintenance Beliefs and Behaviors, Young-Ok Yum, Daniel J. Canary; Part 4 Epilogue; Chapter 14 Framing the Maintenance of Relationships Through Communication: An Epilogue, Marianne Dainton;
£47.49
Taylor & Francis Inc Stereotype Dynamics LanguageBased Approaches to
Book SynopsisThis volume addresses the role of communication in stereotype dynamics, while placing the phenomenon of social stereotypes appropriately in the socio-cultural context.Trade Review"I think it is critically important for social psychologists to focus more on the influence of language and communication across the areas within the discipline, and I believe this volume will stand as a milestone in the movement of social psychology back to studying human interaction." - David Roskos-Ewoldsen, Ph.D., University of Alabama"The authors are all outstanding ... The chapters are timely and important." - Charles Stangor, Ph.D., University of Maryland"… Kashima et al. achieve their goals for this volume… The reader is left with a new appreciation for the social nature of stereotyping, as well as an awareness of the limitations of a strict social cognition perspective… I would recommend this volume for the editors’ intended audience of advanced scholars and students in social psychology, linguistics, and communication." – Matthew L. Newman, PsycCRITIQUES“I think it is critically important for social psychologists to focus more on the influence of language and communication across the areas within the discipline, and I believe this volume will stand as a milestone in the movement of social psychology back to studying human interaction.” —David Roskos-Ewoldsen, Ph.D . University of Alabama“The authors are all outstanding...The chapters are timely and important.” —Charles Stangor, Ph.D. University of MarylandTable of ContentsY. Kashima, K. Fiedler, P. Freytag, Stereotype Dynamics: An Introduction and Overview. Part 1. Stereotype Dynamics.G. Semin, Stereotypes in the Wild. V. Yzerbyt, A. Carnaghi, Stereotype Change in the Social Context. A. Lyons, A. Clark, Y. Kashima, T. Kurz, Cultural Dynamics of Stereotyping. Part 2. Symbolic Mediation and Stereotyping.K. Fiedler, M. Blümke, P. Freytag, S. Koch, C. Unkelbach, A Semiotic Approach to Understanding the Role of Communication in Stereotyping. A. Carnaghi, A. Maass, Derogatory Language in Intergroup Context: Are “Gay” and “Fag” Synonymous? S. Sczesny, J. Bosak, A.B. Diekman, J. Twenge, Dynamics of Sex Role Stereotypes. Part 3. Stereotype and Language Use.C. Wenneker, D. Wigboldus, Interpersonal Consequences and Intrapersonal Underpinnings of the Linguistic Expectancy Bias. K.M. Douglas, R.M. Sutton, C. McGarty, Strategic Language Use in Interpersonal and Intergroup Communication. P. Freytag, Sender-Receiver-Constellations as a Moderator of Linguistic Abstraction Biases. Part 4. Stereotype Sharedness and Distinctiveness.M. Karasawa, S. Suga, Retention and Transmission of Socially Shared Beliefs: The Role of Linguistic Abstraction in Stereotypic Communication. O. Klein, S. Tindale, M. Brauer, The Consensualization of Stereotypes in Small Groups. F. Pratto, P.J. Hegarty, J.D. Korchmaros, How Communication Practices and Category Norms Lead People to Stereotype Particular People and Groups. Part 5. Identity, Self-Regulation, and Stereotyping.M. Hornsey, Intergroup Sensitivity Effect: Responses to Criticisms of Groups. R.M. Sutton, K.M. Douglas, T.J. Elder, M. Tarrant, Social Identity and Social Convention in Responses to Criticisms of Groups. J. Keller, H. Bless, Communicating Stereotype Expectancies: The Interplay of Stereotype Threat and Regulatory Focus.
£137.75
Taylor & Francis Inc Handbook of Relationship Initiation
Book SynopsisThe Handbook of Relationship Initiation is the first volume to focus specifically on the very beginning stage of relationships â their origin. In this Handbook, leading scholars on relationships review the literature on various processes related to the initiation of relationships: how people meet, communicate for the first time, and begin to define themselves as being in a relationship. Topics include attraction, mate selection, influence of social networks on relationship initiation, initiation over the internet, hook-ups among young adults, and flirting and opening gambits. In addition, the dark side of relationship initiation is considered, including unwanted relationship pursuit and barriers to relationship initiation including social anxiety.This volume provides an overdue synthesis of the literature on this topic. It is especially timely in view of the growing prevalence on relationship initiation online, through matchmaking and other social networking sites, which has increased awareness that science can be used to understand, create, and facilitate compatible matching.This Handbook provides an essential resource for an interdisciplinary range of researchers and students who study relationships, including social psychologists, communication scientists and scholars of marriage and the family.Trade Review"I am somewhat chagrined to find that after 20 years in the field, I found a great deal that I did not know regarding relationship initiation. ... I strongly suspect that this latest work will be an instant classic. ... I highly recommend the handbook for relationship scholars from a variety of disciplines. It is also appropriate for graduate students and upper level undergraduates." - Gregory D. Morrow, Edinboro University of Pennsylvania, in PsycCRITIQUESTable of ContentsPart 1. Introduction. S. Sprecher, A. Wenzel, J. Harvey, Preface. C. A. Bredow, R. M. Cate, T. L. Huston, Have We Met Before? A Conceptual Model of First Romantic Encounters. B. Fehr, Friendship Formation. D. P. Schmitt, An Evolutionary Perspective on Mate Choice and Relationship Initiation. G. Creasey, P. Jarvis, Attachment Theory and Research: A Special Focus on Relationship Initiation. Part 2. The Process of Relationship Initiation. M. R. Cunningham, A. P. Barbee, Prelude to a Kiss: Nonverbal Flirting, Opening Gambits, and Other Communication Dynamics in the Initiation of Romantic Relationships. L. K. Knoblock, L. E. Miller, Uncertainty and Relationship Initiation. W. A. Afifi, A. A. Lucas, Information Seeking in Initial Stages of Relational Development. V. J. Derlega, B. A. Winstead, K. Greene, Self-Disclosure and Starting a Close Relationship. L. K. Guerrero, P. A. Mongeau, On Becoming "More than Friends": The Transition from Friendship to Romantic Relationship. Part 3. Diverse Contexts of Relationship Initiation. X. B. Arriaga, C. R. Agnew, N. M. Capezza, J. J. Lehmiller, The Social and Physical Environment of Relationship Initiation: An Interdependence Analysis. P. W. Eastwick, E. J. Finkel, Speed-Dating: A Powerful and Flexible Paradigm for Studying Relationship Initiation. K. Y. A. McKenna, MySpace or Your Place: Relationship Initiation and Development in the Wired and Wireless World. S. Sprecher, P. Schwartz, J. Harvey, E. Hatfield, Thebusinessoflove.com: Relationship Initiation at Internet Matchmatching Services. Part 4. Attraction and Other Emotions in Relationship Initiation. J. W. Bruce, W. G. Graziano, Attraction and the Initiation of Relationships: A Review of the Empirical Literature. S. Sprecher, D. Felmlee, Insider Perspectives to Attraction. A. Aron, H. E. Fisher, G. Strong, B. Acevedo, S. Riela, I. Tsapelas, Falling in Love. S. S. Hencrick, C. Hendrick, Satisfaction, Love, and Respect in the Initiation of Romantic Relationships. S. Metts, S. L. Mikucki, The Emotional Landscape of Relationship Initiation. Part 5. Challenges and Problematic Relationship Initiation. E. L. Paul, A. Wenzel, J. H. Harvey, Hookups: A Facilitator or a Barrier to Relationship Initiation and Intimacy Development? M. A. Fine, T. A. Coffelt, L. N. Olson, Romantic Relationship Initiation following Relationship Dissolution. W. R. Cupach, B. H. Spitzberg, "Thanks, but No Thanks…." The Occurrence and Management of Unwanted Relationship Pursuit. A. Wenzel, T. B. Kashdan, Emotional Disturbances and the Initial Stages of Relationship Development: Processes and Consequences of Social Anxiety and Depression. Part 6. Cognitions, Beliefs, and Memories About Relationship Initiation. L. Custer, D. Holmberg, K. Blair, T. L. Orbuch, "So How Did You Two Meet?": Narratives of Relationship Initiation. C. R. Knee, A. L. Bush, Relationship Beliefs and Their Role in Relationship Initiation. S. Tran, J. A. Simpson, G. J. O. Fletcher, The Role of Ideal Standards in Relationship Initiation Processes. G. D. Reeder, Perceptions of Goals and Motives in Romantic Relationships. Part 7. Commentary. D. Perlman, Ending the Beginning of Relationships.
£128.25
Springer Classical Topology and Combinatorial Group Theory
Book Synopsis0 Introduction and Foundations.- 0.1 The Fundamental Concepts and Problems of Topology.- 0.2 Simplicial Complexes.- 0.3 The Jordan Curve Theorem.- 0.4 Algorithms.- 0.5 Combinatorial Group Theory.- 1 Complex Analysis and Surface Topology.- 1.1 Riemann Surfaces.- 1.2 Nonorientable Surfaces.- 1.3 The Classification Theorem for Surfaces.- 1.4 Covering Surfaces.- 2 Graphs and Free Groups.- 2.1 Realization of Free Groups by Graphs.- 2.2 Realization of Subgroups.- 3 Foundations for the Fundamental Group.- 3.1 The Fundamental Group.- 3.2 The Fundamental Group of the Circle.- 3.3 Deformation Retracts.- 3.4 The SeifertVan Kampen Theorem.- 3.5 Direct Products.- 4 Fundamental Groups of Complexes.- 4.1 Poincaré's Method for Computing Presentations.- 4.2 Examples.- 4.3 Surface Complexes and Subgroup Theorems.- 5 Homology Theory and Abelianization.- 5.1 Homology Theory.- 5.2 The Structure Theorem for Finitely Generated Abelian Groups.- 5.3 Abelianization.- 6 Curves on Surfaces.- 6.1 Dehn's Algorithm.Table of Contents0 Introduction and Foundations.- 0.1 The Fundamental Concepts and Problems of Topology.- 0.2 Simplicial Complexes.- 0.3 The Jordan Curve Theorem.- 0.4 Algorithms.- 0.5 Combinatorial Group Theory.- 1 Complex Analysis and Surface Topology.- 1.1 Riemann Surfaces.- 1.2 Nonorientable Surfaces.- 1.3 The Classification Theorem for Surfaces.- 1.4 Covering Surfaces.- 2 Graphs and Free Groups.- 2.1 Realization of Free Groups by Graphs.- 2.2 Realization of Subgroups.- 3 Foundations for the Fundamental Group.- 3.1 The Fundamental Group.- 3.2 The Fundamental Group of the Circle.- 3.3 Deformation Retracts.- 3.4 The Seifert—Van Kampen Theorem.- 3.5 Direct Products.- 4 Fundamental Groups of Complexes.- 4.1 Poincaré’s Method for Computing Presentations.- 4.2 Examples.- 4.3 Surface Complexes and Subgroup Theorems.- 5 Homology Theory and Abelianization.- 5.1 Homology Theory.- 5.2 The Structure Theorem for Finitely Generated Abelian Groups.- 5.3 Abelianization.- 6 Curves on Surfaces.- 6.1 Dehn’s Algorithm.- 6.2 Simple Curves on Surfaces.- 6.3 Simplification of Simple Curves by Homeomorphisms.- 6.4 The Mapping Class Group of the Torus.- 7 Knots and Braids.- 7.1 Dehn and Schreier’s Analysis of the Torus Knot Groups.- 7.2 Cyclic Coverings.- 7.3 Braids.- 8 Three-Dimensional Manifolds.- 8.1 Open Problems in Three-Dimensional Topology.- 8.2 Polyhedral Schemata.- 8.3 Heegaard Splittings.- 8.4 Surgery.- 8.5 Branched Coverings.- 9 Unsolvable Problems.- 9.1 Computation.- 9.2 HNN Extensions.- 9.3 Unsolvable Problems in Group Theory.- 9.4 The Homeomorphism Problem.- Bibliography and Chronology.
£50.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG p-Adic Lie Groups
Book SynopsisManifolds over complete nonarchimedean fields together with notions like tangent spaces and vector fields form a convenient geometric language to express the basic formalism of p-adic analysis. The volume starts with a self-contained and detailed introduction to this language. This includes the discussion of spaces of locally analytic functions as topological vector spaces, important for applications in representation theory. The author then sets up the analytic foundations of the theory of p-adic Lie groups and develops the relation between p-adic Lie groups and their Lie algebras. The second part of the book contains, for the first time in a textbook, a detailed exposition of Lazard's algebraic approach to compact p-adic Lie groups, via his notion of a p-valuation, together with its application to the structure of completed group rings.Trade ReviewFrom the reviews:“The book is divided into two parts … . The author’s style of writing is elegant … . this is a demanding book, but a rewarding one … . any person who intends to work in this area will want to have it close at hand.” (Mark Hunacek, The Mathematical Gazette, Vol. 98 (541), March, 2014)“This book presents the foundations of the theory of p-adic Lie groups in a systematic and self-contained way. … Schneider’s book on p-adic Lie groups systematically develops the analytic theory of p-adic Lie groups and also Lazard’s algebraic approach to p-adic Lie groups. It is highly recommended.” (Dubravka Ban, Mathematical Reviews, Issue 2012 h)“The notion of a p-adic Lie group has been around for a while, but they have recently become more prominent in number theory and representation theory. … Schneider’s Grundlehren volume is an attempt to fill that gap by giving a systematic treatment of the subject. … this is a book to be welcomed and studied carefully by anyone who wants to learn about p-adic Lie theory.” (Fernando Q. Gouvêa, The Mathematical Association of America, August, 2011)“The book thoroughly discusses the analytic aspects of p-adic manifolds and p-adic lie groups. … this clearly written book by Schneider will be very useful … to all those interested learning the basic theory of p-adic groups or about the completed group ring of a p-adic group with number theoretical applications in mind.” (Bala Sury, Zentralblatt MATH, Vol. 1223, 2011)Table of ContentsIntroduction.- Part A: p-Adic Analysis and Lie Groups.- I.Foundations.- I.1.Ultrametric Spaces.- I.2.Nonarchimedean Fields.- I.3.Convergent Series.- I.4.Differentiability.- I.5.Power Series.- I.6.Locally Analytic Functions.- II.Manifolds.- II.7.Charts and Atlases.- II.8.Manifolds.- II.9.The Tangent Space.- II.10.The Topological Vector Space C^an(M,E), part 1.- II.11 Locally Convex K-Vector Spaces.- II.12 The Topological Vector Space C^an(M,E), part 2.- III.Lie Groups.- III.13.Definitions and Foundations.- III.14.The Universal Enveloping Algebra.- III.15.The Concept of Free Algebras.- III.16.The Campbell-Hausdorff Formula.- III.17.The Convergence of the Hausdorff Series.- III.18.Formal Group Laws.- Part B:The Algebraic Theory of p-Adic Lie Groups.- IV.Preliminaries.- IV.19.Completed Group Rings.- IV.20.The Example of the Group Z^d_p.- IV.21.Continuous Distributions.- IV.22.Appendix: Pseudocompact Rings.- V.p-Valued Pro-p-Groups.- V.23.p-Valuations.- V.24.The free Group on two Generators.- V.25.The Operator P.- V.26.Finite Rank Pro-p-Groups.- V.27.Compact p-Adic Lie Groups.- VI.Completed Group Rings of p-Valued Groups.- VI.28.The Ring Filtration.- VI.29.Analyticity.- VI.30.Saturation.- VII.The Lie Algebra.- VII.31.A Normed Lie Algebra.- VII.32.The Hausdorff Series.- VII.33.Rational p-Valuations and Applications.- VII.34.Coordinates of the First and of the Second Kind.- References.- Index.
£84.99
The University of Chicago Press Topics in Geometric Group Theory
Book SynopsisThis work seeks to offer a concise introduction to geometric group theory - a method for studying infinite groups via their intrinsic geometry. Basic combinatorial and geometric group theory is presented, along with research on the growth of groups, and exercises and problems.
£34.20
