An Introduction to K-Theory for C*-Algebras (London Mathematical Society Student Texts)
Cambridge University Press, 8/21/2008
EAN 9780521789448, ISBN10: 0521789443
Paperback, 256 pages, 22.8 x 15.2 x 1.5 cm
Language: English
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.
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.