An introduction to the classification of amenable C*-algebras

書誌事項

An introduction to the classification of amenable C*-algebras

Huaxin Lin

World Scientific, c2001

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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
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