An Introduction to the Classification of Amenable C*-Algebras (Hardcover) (ISBN-13: 9789810246808)

The theory and applications of C∗-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C∗-algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C∗-algebras (up to isomorphism) by their K-theoretical data. It started with the classification of AT-algebras with real rank zero. Since then great efforts have been made to classify amenable C∗-algebras, a class of C∗-algebras that arises most naturally. For example, a large class of simple amenable C∗-algebras is discovered to be classifiable. The application of these results to dynamical systems has been established.This book introduces the recent development of the theory of the classification of amenable C∗-algebras -- the first such attempt. The first three chapters present the basics of the theory of C∗-algebras which are particularly important to the theory of the classification of amenable C∗-algebras. Chapter 4 otters the classification of the so-called AT-algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C∗-algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH-algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C∗-algebras. Besides being as an introduction to the theory of the classification of amenable C∗-algebras, it is a comprehensive reference for those more familiar with the subject.

Author: Huaxin Lin
ISBN-10: 9810246803
ISBN-13: 9789810246808
Publisher: World Scientific Publishing Company
Language: English
Published: 11/12/2001
Pages: 332
Format: Hardcover
Weight: 1.23lbs
Size: 8.60h x 6.10w x 0.90d