Description

Book Synopsis
Over the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics. Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C*-algebra A. These groups reflect the properties of A in many ways. This book covers the basic properties of the functors K0 and K1 and their interrelationship. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each pair of countable Abelian groups arises as the K-groups of some C*-algebra. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students working in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.

Trade Review
'The textbook is a nice introduction to the subject preparing the ground for the study of more advanced texts.' H. Schröder, Zentralblatt für Mathematik

Table of Contents
Preface; 1. C*-algebra theory; 2. Projections and unitary elements; 3. The K0-group of a unital C*-algebra; 4. The functor K0; 5. The ordered Abelian group K0(A); 6. Inductive limit C*-algebras; 7. Classification of AF-algebras; 8. The functor K1; 9. The index map; 10. The higher K-functors; 11. Bott periodicity; 12. The six-term exact sequence; 13. Inductive limits of dimension drop algebras; References; Table of K-groups; Index of symbols; General index.

An Introduction to KTheory for CAlgebras 49 London Mathematical Society Student Texts Series Number 49

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    A Hardback by M. Rørdam, F. Larsen, N. Laustsen

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      Book details

      Publisher Cambridge University Press
      Published 7/20/2000 12:00:00 AM
      ISBN-13 9780521783347
      978-0521783347
      ISBN-10 0521783348
      Also in:
      Algebra

      Description

      Book Synopsis
      Over the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics. Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C*-algebra A. These groups reflect the properties of A in many ways. This book covers the basic properties of the functors K0 and K1 and their interrelationship. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each pair of countable Abelian groups arises as the K-groups of some C*-algebra. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students working in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.

      Trade Review
      'The textbook is a nice introduction to the subject preparing the ground for the study of more advanced texts.' H. Schröder, Zentralblatt für Mathematik

      Table of Contents
      Preface; 1. C*-algebra theory; 2. Projections and unitary elements; 3. The K0-group of a unital C*-algebra; 4. The functor K0; 5. The ordered Abelian group K0(A); 6. Inductive limit C*-algebras; 7. Classification of AF-algebras; 8. The functor K1; 9. The index map; 10. The higher K-functors; 11. Bott periodicity; 12. The six-term exact sequence; 13. Inductive limits of dimension drop algebras; References; Table of K-groups; Index of symbols; General index.

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