An Introduction to the Classification of Amenable C-Algebras [Hardcover]

Huaxin Lin (Author)

Book Description

ISBN-10: 9810246803 | ISBN-13: 978-9810246808 | Publication Date: November 2001 | Edition: 1st

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 offers 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. As well as providing an introduction to the theory of the classification of amenable C*-algebras, it is a comprehensive reference for those more familiar with the subject.

Editorial Reviews

Review

...an excellent job of introducing some of the recent developments of this theory to a broad range of readers. -- Mathematical Reviews, 2002

...very useful as a possible text for an advanced postgraduate course on the classification of nuclear C*-Algebras. -- Bulletin of the London Mathematical Society, 2003

a well-readable and comprehensive guide for those who want to study and work with this theory. -- Mathematics Abstracts

Product Details

• Hardcover: 332 pages
• Publisher: World Scientific Pub Co Inc; 1st edition (November 2001)
• Language: English
• ISBN-10: 9810246803
• ISBN-13: 978-9810246808
• Product Dimensions: 8.6 x 6.1 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #4,308,621 in Books (See Top 100 in Books)

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