Groups and group theory Books
Taylor & Francis Ltd Cooperation Psychology Revivals
a huge range and FREE tracked UK delivery on ALL orders.
£112.00
Taylor & Francis Ltd Cooperation Psychology Revivals
a huge range and FREE tracked UK delivery on ALL orders.
£41.64
Taylor & Francis The Scientific Study of Social Behaviour Psychology Revivals
a huge range and FREE tracked UK delivery on ALL orders.
£142.50
Taylor & Francis The Scientific Study of Social Behaviour Psychology Revivals
a huge range and FREE tracked UK delivery on ALL orders.
£53.99
Taylor & Francis Managing Interpersonal Conflict
a huge range and FREE tracked UK delivery on ALL orders.
£58.99
Cambridge University Press Kleinian Groups and Hyperbolic 3Manifolds Proceedings of the Warwick Workshop September 1114 2001 299 London Mathematical Society Lecture Note Series Series Number 299
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
Springer NonAssociative Algebra and Its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
Taylor & Francis Personal Relationships and Personal Networks LEAs Series on Personal Relationships
a huge range and FREE tracked UK delivery on ALL orders.
£135.00
Taylor & Francis Cultural Communication and Intercultural Contact
a huge range and FREE tracked UK delivery on ALL orders.
£48.44
Taylor & Francis Confrontation Talk
a huge range and FREE tracked UK delivery on ALL orders.
£36.99
Taylor & Francis Groups at Work Theory and Research Applied Social Research Series
a huge range and FREE tracked UK delivery on ALL orders.
£84.99
Taylor & Francis Groups at Work Theory and Research Applied Social Research Series
a huge range and FREE tracked UK delivery on ALL orders.
£135.00
Taylor & Francis Interpersonal Sensitivity Theory and Measurement Personality Clinical Psychology Hardcover
a huge range and FREE tracked UK delivery on ALL orders.
£118.75
Taylor & Francis Explaining Communication Contemporary Theories and Exemplars Routledge Communication Series
a huge range and FREE tracked UK delivery on ALL orders.
£71.99
Taylor & Francis Handbook of Affect and Social Cognition
a huge range and FREE tracked UK delivery on ALL orders.
£64.99
Taylor & Francis Nonverbal Communication in Close Relationships LEAs Series on Personal Relationships
a huge range and FREE tracked UK delivery on ALL orders.
£39.99
Taylor & Francis Nonverbal Communication in Close Relationships LEAs Series on Personal Relationships
a huge range and FREE tracked UK delivery on ALL orders.
£135.00
Taylor & Francis Maintaining LongDistance and CrossResidential Relationships Routledge Communication Series
a huge range and FREE tracked UK delivery on ALL orders.
£152.56
Taylor & Francis Communicating at the End of Life Finding Magic in the Mundane LEAs Series on Personal Relationships
a huge range and FREE tracked UK delivery on ALL orders.
£135.00
Taylor & Francis Communicating at the End of Life Finding Magic in the Mundane LEAs Series on Personal Relationships
a huge range and FREE tracked UK delivery on ALL orders.
£36.99
Taylor & Francis Critical Thinking About Sex Love and Romance in the Mass Media Media Literacy Applications Routledge Communication Series
a huge range and FREE tracked UK delivery on ALL orders.
£54.99
Taylor & Francis The Dark Side Of Interpersonal Communication
a huge range and FREE tracked UK delivery on ALL orders.
£76.99
Taylor & Francis The Dark Side of Interpersonal Communication
a huge range and FREE tracked UK delivery on ALL orders.
£155.00
Taylor & Francis Personal Relationships and Personal Networks LEAs Series on Personal Relationships
a huge range and FREE tracked UK delivery on ALL orders.
£39.99
Taylor & Francis The Social Psychology of Living Well Sydney Symposium of Social Psychology
a huge range and FREE tracked UK delivery on ALL orders.
£58.99
Taylor & Francis The Social Psychology of Living Well Sydney Symposium of Social Psychology
a huge range and FREE tracked UK delivery on ALL orders.
£150.00
Taylor & Francis Personal Relationships
a huge range and FREE tracked UK delivery on ALL orders.
£47.99
Taylor & Francis Inc Differential Equations and Group Methods for Scientists and Engineers
a huge range and FREE tracked UK delivery on ALL orders.
£195.06
Springer Representations of Hecke Algebras at Roots of Unity 15 Algebra and Applications
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
Springer On Normalized Integral Table Algebras Fusion Rings Generated by a Faithful Nonreal Element of Degree 3 16 Algebra and Applications
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
Taylor & Francis Ltd Complex Interpersonal Conflict Behaviour Theoretical Frontiers Essays in Social Psychology
a huge range and FREE tracked UK delivery on ALL orders.
£135.00
Taylor & Francis New Perspectives in Early Communicative Development 8 Psychology Library Editions Child Development
a huge range and FREE tracked UK delivery on ALL orders.
£120.00
Springer New York Linear Algebraic Groups
Book SynopsisAGBackground Material From Algebraic Geometry.- 1. Some Topological Notions.- 2. Some Facts from Field Theory.- 3. Some Commutative Algebra.- 4. Sheaves.- 5. Affine K-Schemes, Prevarieties.- 6. Products; Varieties.- 7. Projective and Complete Varieties.- 8. Rational Functions; Dominant Morphisms.- 9. Dimension.- 10. Images and Fibres of a Morphism.- 11. k-structures on K-Schemes.- 12. k-Structures on Varieties.- 13. Separable points.- 14. Galois Criteria for Rationality.- 15. Derivations and Differentials.- 16. Tangent Spaces.- 17. Simple Points.- 18. Normal Varieties.- References.- IGeneral Notions Associated With Algebraic Groups.- 1. The Notion of an Algebraic Groups.- 2. Group Closure; Solvable and Nilpotent Groups.- 3. The Lie Algebra of an Algebraic Group.- 4. Jordan Decomposition.- II Homogeneous Spaces.- 5. Semi-Invariants.- 6. Homogeneous Spaces.- 7. Algebraic Groups in Characteristic Zero.- III Solvable Groups.- 8. Diagonalizable Groups and Tori.- 9. Conjugacy Classes and Centralizers of Semi-Simple Elements.- 10. Connected Solvable Groups.- IVBorel Subgroups; Reductive Groups.- 11. Borel Subgroups.- 12. Cartan Subgroups; Regular Elements.- 13. The Borel Subgroups Containing a Given Torus.- 14. Root Systems and Bruhat Decomposition in Reductive Groups.- VRationality Questions.- 15. Split Solvable Groups and Subgroups.- 16. Groups over Finite Fields.- 17. Quotient of a Group by a Lie Subalgebra.- 18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups.- 19. Cartan Subgroups of Solvable Groups.- 20. Isotropic Reductive Groups.- 21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups.- 22. Central Isogenies.- 23. Examples.- 24. Survey of Some Other Topics.- A. Classification.- B. Linear Representations.- C. Real Reductive Groups.- References for Chapters I to V.- Index of Definition.- Index of Notation.Table of ContentsAG—Background Material From Algebraic Geometry.- §1. Some Topological Notions.- §2. Some Facts from Field Theory.- §3. Some Commutative Algebra.- §4. Sheaves.- §5. Affine K-Schemes, Prevarieties.- §6. Products; Varieties.- §7. Projective and Complete Varieties.- §8. Rational Functions; Dominant Morphisms.- §9. Dimension.- §10. Images and Fibres of a Morphism.- §11. k-structures on K-Schemes.- §12. k-Structures on Varieties.- §13. Separable points.- §14. Galois Criteria for Rationality.- §15. Derivations and Differentials.- §16. Tangent Spaces.- §17. Simple Points.- §18. Normal Varieties.- References.- I—General Notions Associated With Algebraic Groups.- §1. The Notion of an Algebraic Groups.- §2. Group Closure; Solvable and Nilpotent Groups.- §3. The Lie Algebra of an Algebraic Group.- §4. Jordan Decomposition.- II — Homogeneous Spaces.- §5. Semi-Invariants.- §6. Homogeneous Spaces.- §7. Algebraic Groups in Characteristic Zero.- III Solvable Groups.- §8. Diagonalizable Groups and Tori.- §9. Conjugacy Classes and Centralizers of Semi-Simple Elements.- §10. Connected Solvable Groups.- IV—Borel Subgroups; Reductive Groups.- §11. Borel Subgroups.- §12. Cartan Subgroups; Regular Elements.- §13. The Borel Subgroups Containing a Given Torus.- §14. Root Systems and Bruhat Decomposition in Reductive Groups.- V—Rationality Questions.- §15. Split Solvable Groups and Subgroups.- §16. Groups over Finite Fields.- §17. Quotient of a Group by a Lie Subalgebra.- §18. Cartan Subgroups over the Groundfield. Unirationality. Splitting of Reductive Groups.- §19. Cartan Subgroups of Solvable Groups.- §20. Isotropic Reductive Groups.- §21. Relative Root System and Bruhat Decomposition for Isotropic Reductive Groups.- §22. Central Isogenies.- §23. Examples.- §24. Survey of Some Other Topics.- A. Classification.- B. Linear Representations.- C. Real Reductive Groups.- References for Chapters I to V.- Index of Definition.- Index of Notation.
£999.99
Springer New York Linear Algebraic Groups 21 Graduate Texts in Mathematics
Book SynopsisHe has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.Trade ReviewJ.E. Humphreys Linear Algebraic Groups "Exceptionally well-written and ideally suited either for independent reading or as a graduate level text for an introduction to everything about linear algebraic groups."—MATHEMATICAL REVIEWSTable of ContentsI. Algebraic Geometry.- 0. Some Commutative Algebra.- 1. Affine and Projective Varieties.- 1.1 Ideals and Affine Varieties.- 1.2 Zariski Topology on Affine Space.- 1.3 Irreducible Components.- 1.4 Products of Affine Varieties.- 1.5 Affine Algebras and Morphisms.- 1.6 Projective Varieties.- 1.7 Products of Projective Varieties.- 1.8 Flag Varieties.- 2. Varieties.- 2.1 Local Rings.- 2.2 Prevarieties.- 2.3 Morphisms.- 2.4 Products.- 2.5 Hausdorff Axiom.- 3. Dimension.- 3.1 Dimension of a Variety.- 3.2 Dimension of a Subvariety.- 3.3 Dimension Theorem.- 3.4 Consequences.- 4. Morphisms.- 4.1 Fibres of a Morphism.- 4.2 Finite Morphisms.- 4.3 Image of a Morphism.- 4.4 Constructible Sets.- 4.5 Open Morphisms.- 4.6 Bijective Morphisms.- 4.7 Birational Morphisms.- 5. Tangent Spaces.- 5.1 Zariski Tangent Space.- 5.2 Existence of Simple Points.- 5.3 Local Ring of a Simple Point.- 5.4 Differential of a Morphism.- 5.5 Differential Criterion for Separability.- 6. Complete Varieties.- 6.1 Basic Properties.- 6.2 Completeness of Projective Varieties.- 6.3 Varieties Isomorphic to P1.- 6.4 Automorphisms of P1.- II. Affine Algebraic Groups.- 7. Basic Concepts and Examples.- 7.1 The Notion of Algebraic Group.- 7.2 Some Classical Groups.- 7.3 Identity Component.- 7.4 Subgroups and Homomorphisms.- 7.5 Generation by Irreducible Subsets.- 7.6 Hopf Algebras.- 8. Actions of Algebraic Groups on Varieties.- 8.1 Group Actions.- 8.2 Actions of Algebraic Groups.- 8.3 Closed Orbits.- 8.4 Semidirect Products.- 8.5 Translation of Functions.- 8.6 Linearization of Affine Groups.- III. Lie Algebras.- 9. Lie Algebra of an Algebraic Group.- 9.1 Lie Algebras and Tangent Spaces.- 9.2 Convolution.- 9.3 Examples.- 9.4 Subgroups and Lie Subalgebras.- 9.5 Dual Numbers.- 10. Differentiation.- 10.1 Some Elementary Formulas.- 10.2 Differential of Right Translation.- 10.3 The Adjoint Representation.- 10.4 Differential of Ad.- 10.5 Commutators.- 10.6 Centralizers.- 10.7 Automorphisms and Derivations.- IV. Homogeneous Spaces.- 11. Construction of Certain Representations.- 11.1 Action on Exterior Powers.- 11.2 A Theorem of Chevalley.- 11.3 Passage to Projective Space.- 11.4 Characters and Semi-Invariants.- 11.5 Normal Subgroups.- 12. Quotients.- 12.1 Universal Mapping Property.- 12.2 Topology of Y.- 12.3 Functions on Y.- 12.4 Complements.- 12.5 Characteristic 0.- V. Characteristic 0 Theory.- 13. Correspondence between Groups and Lie Algebras.- 13.1 The Lattice Correspondence.- 13.2 Invariants and Invariant Subspaces.- 13.3 Normal Subgroups and Ideals.- 13.4 Centers and Centralizers.- 13.5 Semisimple Groups and Lie Algebras.- 14. Semisimple Groups.- 14.1 The Adjoint Representation.- 14.2 Subgroups of a Semisimple Group.- 14.3 Complete Reducibility of Representations.- VI. Semisimple and Unipotent Elements.- 15. Jordan-Chevalley Decomposition.- 15.1 Decomposition of a Single Endomorphism.- 15.2 GL(n, K) and gl(n, K).- 15.3 Jordan Decomposition in Algebraic Groups.- 15.4 Commuting Sets of Endomorphisms.- 15.5 Structure of Commutative Algebraic Groups.- 16. Diagonalizable Groups.- 16.1 Characters and d-Groups.- 16.2 Tori.- 16.3 Rigidity of Diagonalizable Groups.- 16.4 Weights and Roots.- VII. Solvable Groups.- 17. Nilpotent and Solvable Groups.- 17.1 A Group-Theoretic Lemma.- 17.2 Commutator Groups.- 17.3 Solvable Groups.- 17.4 Nilpotent Groups.- 17.5 Unipotent Groups.- 17.6 Lie-Kolchin Theorem.- 18. Semisimple Elements.- 18.1 Global and Infinitesimal Centralizers.- 18.2 Closed Conjugacy Classes.- 18.3 Action of a Semisimple Element on a Unipotent Group.- 18.4 Action of a Diagonalizable Group.- 19. Connected Solvable Groups.- 19.1 An Exact Sequence.- 19.2 The Nilpotent Case.- 19.3 The General Case.- 19.4 Normalizer and Centralizer.- 19.5 Solvable and Unipotent Radicals.- 20. One Dimensional Groups.- 20.1 Commutativity of G.- 20.2 Vector Groups and e-Groups.- 20.3 Properties of p-Polynomials.- 20.4 Automorphisms of Vector Groups.- 20.5 The Main Theorem.- VIII. Borel Subgroups.- 21. Fixed Point and Conjugacy Theorems.- 21.1 Review of Complete Varieties.- 21.2 Fixed Point Theorem.- 21.3 Conjugacy of Borel Subgroups and Maximal Tori.- 21.4 Further Consequences.- 22. Density and Connectedness Theorems.- 22.1 The Main Lemma.- 22.2 Density Theorem.- 22.3 Connectedness Theorem.- 22.4 Borel Subgroups of CG(S).- 22.5 Cartan Subgroups: Summary.- 23. Normalizer Theorem.- 23.1 Statement of the Theorem.- 23.2 Proof of the Theorem.- 23.3 The variety G/B.- 23.4 Summary.- IX. Centralizers of Tori.- 24. Regular and Singular Tori.- 24.1 Weyl Groups.- 24.2 Regular Tori.- 24.3 Singular Tori and Roots.- 24.4 Regular 1-Parameter Subgroups.- 25. Action of a Maximal Torus on G/?.- 25.1 Action of a 1-Parameter Subgroup.- 25.2 Existence of Enough Fixed Points.- 25.3 Groups of Semisimple Rank 1.- 25.4 Weyl Chambers.- 26. The Unipotent Radical.- 26.1 Characterization of Ru(G).- 26.2 Some Consequences.- 26.3 The Groups U?.- X. Structure of Reductive Groups.- 27. The Root System.- 27.1 Abstract Root Systems.- 27.2 The Integrality Axiom.- 27.3 Simple Roots.- 27.4 The Automorphism Group of a Semisimple Group.- 27.5 Simple Components.- 28. Bruhat Decomposition.- 28.1 T-Stable Subgroups of Bu.- 28.2 Groups of Semisimple Rank 1.- 28.3 The Bruhat Decomposition.- 28.4 Normal Form in G.- 28.5 Complements.- 29. Tits Systems.- 29.1 Axioms.- 29.2 Bruhat Decomposition.- 29.3 Parabolic Subgroups.- 29.4 Generators and Relations for W.- 29.5 Normal Subgroups of G.- 30. Parabolic Subgroups.- 30.1 Standard Parabolic Subgroups.- 30.2 Levi Decompositions.- 30.3 Parabolic Subgroups Associated to Certain Unipotent Groups.- 30.4 Maximal Subgroups and Maximal Unipotent Subgroups.- XI. Representations and Classification of Semisimple Groups.- 31. Representations.- 31.1 Weights.- 31.2 Maximal Vectors.- 31.3 Irreducible Representations.- 31.4 Construction of Irreducible Representations.- 31.5 Multiplicities and Minimal Highest Weights.- 31.6 Contragredients and Invariant Bilinear Forms.- 32. Isomorphism Theorem.- 32.1 The Classification Problem.- 32.2 Extension of ?T to N(T).- 32.3 Extension of ?T to Z?.- 32.4 Extension of ?T to TU?.- 32.5 Extension of ?T to ?.- 32.6 Multiplicativity of ?.- 33. Root Systems of Rank 2.- 33.1 Reformulation of (?), (?), (?).- 33.2 Some Preliminaries.- 33.3 Type A2.- 33.4 Type B2.- 33.5 Type G2.- 33.6 The Existence Problem.- XII. Survey of Rationality Properties.- 34. Fields of Definition.- 34.1 Foundations.- 34.2 Review of Earlier Chapters.- 34.3 Tori.- 34.4 Some Basic Theorems.- 34.5 Borel-Tits Structure Theory.- 34.6 An Example: Orthogonal Groups.- 35. Special Cases.- 35.1 Split and Quasisplit Groups.- 35.2 Finite Fields.- 35.3 The Real Field.- 35.4 Local Fields.- 35.5 Classification.- Appendix. Root Systems.- Index of Terminology.- Index of Symbols.
£44.99
Springer Nature Switzerland AG Groups and Symmetries: From Finite Groups to Lie Groups
Book Synopsis- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self studyTrade Review“The book is very clear and easy to read linearly … . The reader can also cement their understanding with exercises at the end of each chapter, and the book concludes with with an epilogue of worked problems which allow a deeper dive in various directions. … the book is also a great starting point for those with some training in mathematics or physics who wish to broaden their horizons.” (Alastair Litterick, zbMATH 1514.20003, 2023)Table of ContentsIntroduction.- 1. General Facts About Groups.- 2. Representations of Finite Groups.- 3. Representations of Compact Groups.- 4. Lie Groups and Lie Algebras.- 5. Lie Groups SU(2) and SO(3).- 6. Representations of SU(2) and SO(3).- 7. Spherical Harmonics.- 8. Representations of SU(3) and Quarks.- 9. Spin Groups and Spinors.- Problems and Solutions.- Endnote.- Bibliography.-Index.
£37.99
Springer International Publishing AG Handbook of Geometry and Topology of Singularities VIII
£125.99
Springer International Publishing AG Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Book SynopsisThis textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.Review of the first edition:This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.— The Mathematical GazetteTrade Review“The first edition of this book was very good; the second is even better, and more versatile. This text remains one of the most attractive sources available from which to learn elementary Lie group theory, and is highly recommended.” (Mark Hunacek, The Mathematical Gazette, Vol. 101 (551), July, 2017)Table of ContentsPart I: General Theory.-Matrix Lie Groups.- The Matrix Exponential.- Lie Algebras.- Basic Representation Theory.- The Baker–Campbell–Hausdorff Formula and its Consequences.- Part II: Semisimple Lie Algebras.- The Representations of sl(3;C).-Semisimple Lie Algebras.- Root Systems.- Representations of Semisimple Lie Algebras.- Further Properties of the Representations.- Part III: Compact lie Groups.- Compact Lie Groups and Maximal Tori.- The Compact Group Approach to Representation Theory.- Fundamental Groups of Compact Lie Groups.- Appendices.
£999.99
Springer International Publishing AG Quantum Theory, Groups and Representations: An Introduction
Book SynopsisThis text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.Trade Review“The book presents a large variety of important subjects, including the basic principles of quantum mechanics … . This good book is recommended for mathematicians, physicists, philosophers of physics, researchers, and advanced students in mathematics and physics, as well as for readers with some elementary physics, multivariate calculus and linear algebra courses.” (Michael M. Dediu, Mathematical Reviews, June, 2018)Table of ContentsPreface.- 1 Introduction and Overview.- 2 The Group U(1) and its Representations.- 3 Two-state Systems and SU(2).- 4 Linear Algebra Review, Unitary and Orthogonal Groups.- 5 Lie Algebras and Lie Algebra Representations.- 6 The Rotation and Spin Groups in 3 and 4 Dimensions.- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field.- 8 Representations of SU(2) and SO(3).- 9 Tensor Products, Entanglement, and Addition of Spin.- 10 Momentum and the Free Particle.- 11 Fourier Analysis and the Free Particle.- 12 Position and the Free Particle.- 13 The Heisenberg group and the Schrödinger Representation.- 14 The Poisson Bracket and Symplectic Geometry.- 15 Hamiltonian Vector Fields and the Moment Map.- 16 Quadratic Polynomials and the Symplectic Group.- 17 Quantization.- 18 Semi-direct Products.- 19 The Quantum Free Particle as a Representation of the Euclidean Group.- 20 Representations of Semi-direct Products.- 21 Central Potentials and the Hydrogen Atom.- 22 The Harmonic Oscillator.- 23 Coherent States and the Propagator for the Harmonic Oscillator.- 24 The Metaplectic Representation and Annihilation and Creation Operators, d = 1.- 25 The Metaplectic Representation and Annihilation and Creation Operators, arbitrary d.- 26 Complex Structures and Quantization.- 27 The Fermionic Oscillator.- 28 Weyl and Clifford Algebras.- 29 Clifford Algebras and Geometry.- 30 Anticommuting Variables and Pseudo-classical Mechanics.- 31 Fermionic Quantization and Spinors.- 32 A Summary: Parallels Between Bosonic and Fermionic Quantization.- 33 Supersymmetry, Some Simple Examples.- 34 The Pauli Equation and the Dirac Operator.- 35 Lagrangian Methods and the Path Integral.- 36 Multi-particle Systems: Momentum Space Description.- 37 Multi-particle Systems and Field Quantization.- 38 Symmetries and Non-relativistic Quantum Fields.- 39 Quantization of Infinite dimensional Phase Spaces.- 40 Minkowski Space and the Lorentz Group.- 41 Representations of the Lorentz Group.- 42 The Poincaré Group and its Representations.- 43 The Klein-Gordon Equation and Scalar Quantum Fields.- 44 Symmetries and Relativistic Scalar Quantum Fields.- 45 U(1) Gauge Symmetry and Electromagnetic Field.- 46 Quantization of the Electromagnetic Field: the Photon.- 47 The Dirac Equation and Spin-1/2 Fields.- 48 An Introduction to the Standard Model.- 49 Further Topics.- A Conventions.- B Exercises.- Index.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Geometric Invariant Theory
Book SynopsisThis standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.Table of Contents0. Preliminaries.- 1. Definitions.- 2. First properties.- 3. Good and bad actions.- 4. Further properties.- 5. Resumé of some results of Grothendieck.- 1. Fundamental theorems for the actions of reductive groups.- 1. Definitions.- 2. The affine case.- 3. Linearization of an invertible sheaf.- 4. The general case.- 5. Functional properties.- 2. Analysis of stability.- 1. A numeral criterion.- 2. The flag complex.- 3. Applications.- 3. An elementary example.- 1. Pre-stability.- 2. Stability.- 4. Further examples.- 1. Binary quantics.- 2. Hypersurfaces.- 3. Counter-examples.- 4. Sequences of linear subspaces.- 5. The projective adjoint action.- 6. Space curves.- 5. The problem of moduli — 1st construction.- 1. General discussion.- 2. Moduli as an orbit space.- 3. First chern classes.- 4. Utilization of 4.6.- 6. Abelian schemes.- 1. Duals.- 2. Polarizations.- 3. Deformations.- 7. The method of covariants — 2nd construction.- 1. The technique.- 2. Moduli as an orbit space.- 3. The covariant.- 4. Application to curves.- 8. The moment map.- 1. Symplectic geometry.- 2. Symplectic quotients and geometric invariant theory.- 3. Kähler and hyperkähler quotients.- 4. Singular quotients.- 5. Geometry of the moment map.- 6. The cohomology of quotients: the symplectic case.- 7. The cohomology of quotients: the algebraic case.- 8. Vector bundles and the Yang-Mills functional.- 9. Yang-Mills theory over Riemann surfaces.- Appendix to Chapter 1.- Appendix to Chapter 2.- Appendix to Chapter 3.- Appendix to Chapter 4.- Appendix to Chapter 5.- Appendix to Chapter 7.- References.- Index of definitions and notations.
£134.99
Springer Verlag Metodi matematici della Fisica
Book SynopsisQuesto libro trae la sua origine dagli appunti preparati per le lezioni di Metodi Matematici della Fisica tenute al Dipartimento di Fisica dell'Università di Pisa, e via via sistemati, raffinati e aggiornati nel corso di molti anni di insegnamento. L'intento generale è di fornire una presentazione per quanto possibile semplice e diretta dei metodi matematici basilari e rilevanti per la Fisica. Anche allo scopo di mantenere questo testo entro i limiti di un manuale di dimensioni contenute e di agevole consultazione, sono stati spesso sacrificati i dettagli tecnici delle dimostrazioni matematiche (o anzi le dimostrazioni per intero) e anche i formalismi eccessivi, che tendono a nascondere la vera natura dei problemi. Al contrario, si è cercato di evidenziare – per quanto possibile – le idee sottostanti e le motivazioni che conducono ai diversi procedimenti. L'obiettivo principale e quello di mettere in condizione chi ha letto questo libro di acquisire gli strumenti adatti e le conoscenze di base che gli permettano di affrontare senza difficoltà anche testi più avanzati e impegnativi. Questa nuova Edizione conserva la struttura generale della prima Edizione, ma è arricchita dall'inserimento di numerosi esempi (e controesempi), con nuove osservazioni e chiarimenti su tutti gli argomenti proposti: Serie di Fourier, Spazi di Hilbert, Operatori lineari, Funzioni di Variabile complessa, Trasformate di Fourier e di Laplace, Distribuzioni. Inoltre, le prime nozioni della Teoria dei Gruppi, delle Algebre di Lie e delle Simmetrie in Fisica (che erano confinate in una Appendice nella Prima Edizione) vengono ora proposte in una forma sensibilmente ampliata, con vari esempi in vista delle applicazioni alla Fisica. In particolare, due nuovi Capitoli sono dedicati allo studio delle proprietà di simmetria dell'atomo di idrogeno e dell'oscillatore armonico in Meccanica Quantistica.Table of Contents1 Spazi a dimensione fiita.- 2 Spazi di Hilbert.- 3 Funzioni di una variabile complessa.- 4 Trasformate di Fourier e Laplace.- 5 Elementi di teoria delle distribuzioni.- 6 Introduzione alla teoria dei gruppi e alle proprietà di simmetria.- Riferimenti bibliografici.- Indice Analitico.
£31.34
Springer New York Spectra of Graphs
Book SynopsisThis book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics.Trade ReviewFrom the reviews:“Algebraic graph theory seeks logical relations between the graph structure and spectrum structure. Viewing graphs as matrices makes graph spectra a rich, nuanced branch of linear algebra, the central undergraduate subject. … the present volume offers the more thorough literature survey. Summing Up: Recommended. Upper-division undergraduates and above.” (D. V. Feldman, Choice, Vol. 49 (11), August, 2012)“This book contains an extensive overview of current topics and recent developments in algebraic graph theory, and has a survey-like appearance. It is aimed primarily at researchers and graduate-level students, as it is based on lecture notes for the course that the authors gave at the Institute for Studies in Theoretical Physics and Mathematics in Tehran in 2006.” (Dragan Stevanović, Zentralblatt MATH, Vol. 1231, 2012)“The theory of graph spectra has been getting increasing attention over the last several years. … This text … moves the study further along and provides an outstanding reference for graduate students and researchers interested in the many applications of these eigenvalues and their associated eigenvectors. … the authors are well-versed in the literature, providing 358 references and frequently noting where their definitions might differ slightly from those of some previous researchers. … the text serves more as a graduate-level monograph … .” (John T. Saccoman, The Mathematical Association of America, May, 2012)Table of ContentsGraph spectrum.- Linear algebra.- Eigenvalues and eigenvectors of graphs.- The second largest eigenvalue.- Trees.- Groups and graphs.- Topology.- Euclidean representations.- Strongly regular graphs.- Regular two-graphs.- Association schemes.- Distance regular graphs. - p-ranks.- Spectral characterizations.- Graphs with few eigenvalues.- References.- Author Index.- Subject Index.
£44.99
De Gruyter Approximations and Endomorphism Algebras of Modules: Volume 1 – Approximations / Volume 2 – Predictions
Book SynopsisThis second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.Trade ReviewI strongly recommend the monograph to anyone who is interested in the modern theory of modules. (pruz), EMS Newsletter 9/2007 All in all, I highly recommend the book to everyone interested in cotorsion pairs, approximation theory, realization of algebras or application of set theory to algebra. Gabor Braun, Zentralblatt MATH 1121/2007 The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory. L'Enseignement Mathematique 3-4/2006
£297.35
De Gruyter Complementation of Normal Subgroups: In Finite Groups
Book SynopsisStarting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. ContentsPrerequisitesThe Schur-Zassenhaus theorem: A bit of history and motivationAbelian and minimal normal subgroupsReduction theoremsSubgroups in the chief series, derived series, and lower nilpotent seriesNormal subgroups with abelian sylow subgroupsThe formation generationGroups with specific classes of subgroups complemented
£90.25
De Gruyter Structure Theory
Book SynopsisThe problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopesLie algebras of special derivationsDerivation simple algebras and modulesSimple Lie algebrasRecognition theoremsThe isomorphism problemStructure of simple Lie algebrasPairings of induced modulesToral rank 1 Lie algebras
£123.98
De Gruyter Classifying the Absolute Toral Rank Two Case
Book SynopsisThe problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. This is the second part of a three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristic > 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic > 3 is given. Contents Tori in Hamiltonian and Melikian algebras1-sectionsSandwich elements and rigid toriTowards graded algebrasThe toral rank 2 case
£123.98
De Gruyter Groups of Prime Power Order. Volume 6
£164.82
£103.55
De Gruyter Modules over Discrete Valuation Rings
Book SynopsisThis book provides the first systematic treatment of modules over discrete valuation domains, which play an important role in various areas of algebra, especially in commutative algebra. Many important results representing the state of the art are presented in the text along with interesting open problems. This updated edition presents new approaches on p-adic integers and modules, and on the determinability of a module by its automorphism group. ContentsPreliminariesBasic factsEndomorphism rings of divisible and complete modulesRepresentation of rings by endomorphism ringsTorsion-free modulesMixed modulesDeterminity of modules by their endomorphism ringsModules with many endomorphisms or automorphisms
£116.85
