Description
Book SynopsisBased on the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented the results on the theory of $C^*$-algebras and von Neumann algebras, together with the work on the classification of $C^*$-algebras.
Table of ContentsC*-algebras: C*-algebras: Definitions and examples C*-algebras: Constructions Positivity in C*-algebras K-theory I Tensor products of C*-algebras Crossed products I Crossed products II: Examples Free products K-theory II: Roots in topology and index theory C*-algebraic K-theory 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 Tomita-Takesaki theory explained Free products of von Neumann algebras Semigroups of endomorphisms of $\mathcal{B}(H)$ Classification of C*-algebras AF-algebras and Bratteli diagrams Classification of amenable C*-algebras I Classification of amenable C*-algebras II Simple AI-algebras 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 Kauffman-Lins recoupling theory Graphs and connections An extension of the recoupling model Relations to minimal models and subfactors Bibliography.
