An introduction to the classification of amenable C*-algebras

著者

• Lin, Huaxin

書誌事項

An introduction to the classification of amenable C*-algebras

Huaxin Lin

World Scientific, c2001

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

• The basics of C*-algebras
• amenable C*-algebras and K-theory
• AF-algebras and ranks of C*-algebras
• classification of simple AT-algebras
• C*-algebra extensions
• classification of simple amenable C*-algebras.

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詳細情報

• NII書誌ID(NCID): BA54850308
• ISBN:
  • 9810246803
• 出版国コード: si
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Singapore
• ページ数/冊数: xi, 320 p.
• 大きさ: 23 cm