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Hardcover ISBN:  9780821808214 
Product Code:  FIM/13 
List Price:  $95.00 
MAA Member Price:  $85.50 
AMS Member Price:  $76.00 
eBook ISBN:  9781470431402 
Product Code:  FIM/13.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Hardcover ISBN:  9780821808214 
eBook ISBN:  9781470431402 
Product Code:  FIM/13.B 
List Price:  $184.00 $139.50 
MAA Member Price:  $165.60 $125.55 
AMS Member Price:  $147.20 $111.60 

Book DetailsFields Institute MonographsVolume: 13; 2000; 323 ppMSC: Primary 46;
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).
ReadershipGraduate students and research mathematicians interested in operator theory.

Table of Contents

Part 1. C*algebras

Chapter 1. C*algebras: Definitions and examples

Chapter 2. C*algebras: Constructions

Chapter 3. Positivity in C*algebras

Chapter 4. Ktheory I

Chapter 5. Tensor products of C*algebras

Chapter 6. Crossed products I

Chapter 7. Crossed products II: Examples

Chapter 8. Free products

Chapter 9. Ktheory II: Roots in topology and index theory

Chapter 10. C*algebraic Ktheory made concrete, or trick or treat with $2 \times 2$ matrix algebras

Chapter 11. Dilation theory

Chapter 12. C*algebras and mathematical physics

Chapter 13. C*algebras and several complex variables

Part 2. Von Neumann algebras

Chapter 14. Basic structure of von Neumann algebras

Chapter 15. von Neumann algebras (Type $II_1$ factors)

Chapter 16. The equivalence between injectivity and hyperfiniteness, part I

Chapter 17. The equivalence between injectivity and hyperfiniteness, part II

Chapter 18. On the Jones index

Chapter 19. Introductory topics on subfactors

Chapter 20. The TomitaTakesaki theory explained

Chapter 21. Free products of von Neumann algebras

Chapter 22. Semigroups of endomorphisms of $\mathcal {B}(H)$

Part 3. Classification of C*algebras

Chapter 23. AFalgebras and Bratteli diagrams

Chapter 24. Classification of amenable C*algebras I

Chapter 25. Classification of amenable C*algebras II

Chapter 26. Simple AIalgebras and the range of the invariant

Chapter 27. Classification of simple purely infinite C*algebras I

Part 4. Hereditary subalgebras of certain simple non real rank zero C*algebras

Chapter 28. Introduction

Chapter 29. The isomorphism theorem

Chapter 30. The range of the invariant

Chapter 31. Bibliography

Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors

Chapter 32. The KauffmanLins recoupling theory

Chapter 33. Graphs and connections

Chapter 34. An extension of the recoupling model

Chapter 35. Relations to minimal models and subfactors


Additional Material

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


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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).
Graduate students and research mathematicians interested in operator theory.

Part 1. C*algebras

Chapter 1. C*algebras: Definitions and examples

Chapter 2. C*algebras: Constructions

Chapter 3. Positivity in C*algebras

Chapter 4. Ktheory I

Chapter 5. Tensor products of C*algebras

Chapter 6. Crossed products I

Chapter 7. Crossed products II: Examples

Chapter 8. Free products

Chapter 9. Ktheory II: Roots in topology and index theory

Chapter 10. C*algebraic Ktheory made concrete, or trick or treat with $2 \times 2$ matrix algebras

Chapter 11. Dilation theory

Chapter 12. C*algebras and mathematical physics

Chapter 13. C*algebras and several complex variables

Part 2. Von Neumann algebras

Chapter 14. Basic structure of von Neumann algebras

Chapter 15. von Neumann algebras (Type $II_1$ factors)

Chapter 16. The equivalence between injectivity and hyperfiniteness, part I

Chapter 17. The equivalence between injectivity and hyperfiniteness, part II

Chapter 18. On the Jones index

Chapter 19. Introductory topics on subfactors

Chapter 20. The TomitaTakesaki theory explained

Chapter 21. Free products of von Neumann algebras

Chapter 22. Semigroups of endomorphisms of $\mathcal {B}(H)$

Part 3. Classification of C*algebras

Chapter 23. AFalgebras and Bratteli diagrams

Chapter 24. Classification of amenable C*algebras I

Chapter 25. Classification of amenable C*algebras II

Chapter 26. Simple AIalgebras and the range of the invariant

Chapter 27. Classification of simple purely infinite C*algebras I

Part 4. Hereditary subalgebras of certain simple non real rank zero C*algebras

Chapter 28. Introduction

Chapter 29. The isomorphism theorem

Chapter 30. The range of the invariant

Chapter 31. Bibliography

Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors

Chapter 32. The KauffmanLins recoupling theory

Chapter 33. Graphs and connections

Chapter 34. An extension of the recoupling model

Chapter 35. Relations to minimal models and subfactors

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