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An Introduction to K-Theory for C*-Algebrasby F. Larsen
Synopses & Reviews
Over the past twenty-five years K-theory has become an integrated part of the study of C*-algebras. This book gives a very elementary introduction to this interesting and rapidly growing area of mathematics. The authors cover the basic properties of the functors K and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequence is derived. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.
This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
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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