An Introduction to K-Theory for C*-Algebras

by M. Rørdam, F. Larsen, N. Laustsen

Overview

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.

Product Details

ISBN-13:	9780521783347
Publisher:	Cambridge University Press
Publication date:	07/20/2000
Series:	London Mathematical Society Student Texts , #49
Pages:	256
Product dimensions:	5.98(w) x 9.02(h) x 0.75(d)

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.

Editorial Reviews

Offers an elementary introduction to -theory for -algebras. Covers basic properties of the functions 0 and 1 and their interrelationship. The Bott periodicity theorem is proved, and the six-term exact sequence is derived. Applications of the theory include Elliott's classification theorem for -algebras. It is shown that each pair of countable Abelian groups arises as the -groups of some -algebra. Includes some 150 exercises and examples. For beginning graduate students working in functional analysis, especially operator algebras, and for mathematical researchers. Rordam is affiliated with the University of Copenhagen. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

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

From the Publisher