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Classification of Nuclear C*-Algebras. Entropy in Operator Algebras

  • Mikael Rørdam
  • Erling Størmer
Book

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 126)

Table of contents

  1. Front Matter
    Pages I-IX

About this book

Introduction

This EMS volume consists of two parts, written by leading scientists in the field of operator algebras and non-commutative geometry. The first part, written by M.Rordam entitled "Classification of Nuclear, Simple C*-Algebras" is on Elliotts classification program. The emphasis is on the classification by Kirchberg and Phillips of Kirchberg algebras: purely infinite, simple, nuclear separable C*-algebras. This classification result is described almost with full proofs starting from Kirchbergs tensor product theorems and Kirchbergs embedding theorem for exact C*-algebras. The classificatin of finite simple C*-algebras starting with AF-algebras, and continuing with AF- and AH-algberas) is covered, but mostly without proofs. The second part, written by E.Stormer entitled "A Survey of Noncommutative Dynamical Entropy" is a survey of the theory of noncommutative entropy of automorphisms of C*-algebras and von Neumann algebras from its initiation by Connes and Stormer in 1975 till 2001. The main definitions and resuls are discussed and illustrated with the key examples in the theory. This book will be useful to graduate students and researchers in the field of operator algebras and related areas.

Keywords

C*-algebras K-theory Volume algebra classifications entropy entropy in C*-dynamical systems purely infinite C*-algebras

Authors and affiliations

  • Mikael Rørdam
    • 1
  • Erling Størmer
    • 2
  1. 1.Dept. of MathematicsUniversity of CopenhagenCopenhagenDenmark
  2. 2.Dept. of MathematicsUniversity of OsloOsloNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04825-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07605-3
  • Online ISBN 978-3-662-04825-2
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site