Fields Institute Monographs 2000; 323 pp; hardcover Volume: 13 ISBN10: 0821808214 ISBN13: 9780821808214 List Price: US$80 Member Price: US$64 Order Code: FIM/13
 This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of \(C^*\)algebras and von Neumann algebras, together with recent work on the classification of \(C^*\)algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature. Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in operator theory. Reviews "Contains ... a nice illustration of Elliott's classification techniques for inductive limits ... richly illustrated article ... on paths on Coxeter diagrams and subfactors ... particularly welcome ... Overall this is a very nicely and surprisingly uniformly written book which is of interest both for the novice and the expert in operator algebras ... It may be hoped that the book will inspire some young researcher to new invention."  CMS Notes Table of Contents C*algebras  C*algebras: Definitions and examples
 C*algebras: Constructions
 Positivity in C*algebras
 Ktheory I
 Tensor products of C*algebras
 Crossed products I
 Crossed products II: Examples
 Free products
 Ktheory II: Roots in topology and index theory
 C*algebraic Ktheory made concrete, or trick or treat with \(2 \times 2\) matrix algebras
 Dilation theory
 C*algebras and mathematical physics
 C*algebras and several complex variables
von Neumann algebras  Basic structure of von Neumann algebras
 von Neumann algebras (Type \(II_1\) factors)
 The equivalence between injectivity and hyperfiniteness, part I
 The equivalence between injectivity and hyperfiniteness, part II
 On the Jones index
 Introductory topics on subfactors
 The TomitaTakesaki theory explained
 Free products of von Neumann algebras
 Semigroups of endomorphisms of \(\mathcal{B}(H)\)
 Classification of C*algebras
 AFalgebras and Bratteli diagrams
 Classification of amenable C*algebras I
 Classification of amenable C*algebras II
 Simple AIalgebras and the range of the invariant
 Classification of simple purely infinite C*algebras I
Hereditary subalgebras of certain simple non real rank zero C*algebras  Preface
 Introduction
 The isomorphism theorem
 The range of the invariant
 Bibliography
Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors  Preface/Acknowledgements
 The KauffmanLins recoupling theory
 Graphs and connections
 An extension of the recoupling model
 Relations to minimal models and subfactors
 Bibliography
