An Introduction to K-Theory for C*-Algebras (Hardcover)

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Since the 1970s, K-theory has become an integrated part of the study of C*-algebras. This text gives an elementary introduction to this area of mathematics. The fundamental property of 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. In this book the authors cover the basic properties of the functors K0 and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequence is derived. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each countable pair of Abelian groups arises as the K-groups of some C*-algebra. The theory is illustrated with 120 exercises and examples, making the work suitable 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.

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Product Description

Since the 1970s, K-theory has become an integrated part of the study of C*-algebras. This text gives an elementary introduction to this area of mathematics. The fundamental property of 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. In this book the authors cover the basic properties of the functors K0 and K1 and their interrelationship. In particular, the Bott periodicity theorem is proved (Atiyah's proof), and the six-term exact sequence is derived. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each countable pair of Abelian groups arises as the K-groups of some C*-algebra. The theory is illustrated with 120 exercises and examples, making the work suitable 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.

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Product Details

General

Imprint

Cambridge UniversityPress

Country of origin

United Kingdom

Series

London Mathematical Society Student Texts

Release date

2001

Availability

Expected to ship within 10 - 15 working days

First published

2000

Authors

, ,

Dimensions

229 x 152 x 19mm (L x W x T)

Format

Hardcover

Pages

256

ISBN-13

978-0-521-78334-7

Barcode

9780521783347

Categories

LSN

0-521-78334-8



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