Hochschild Cohomology of von Neumann Algebras 9780511526190, 0511526199, 9781107362147, 1107362148
237 74 906KB
English Pages 202 Year 1995
Table of contents :
Contents
Preface
0. Introduction
0.1 General Introduction
0.2 The Hochschild Complex
0.3 History
0.4 Averaging
0.5 Contents
0.6 Background
1. Completely Bounded Operators
1.1 Introduction
1.2 Completely Positive Maps
1.3 Completely Bounded Maps
1.4 The Haagerup Tensor Product
1.5 Multilinear Maps
1.6 Automatic Complete Boundedness
1.7 A Projection onto Completely Bounded Module Maps
1.8 Notes and Remarks
2. Derivations
2.1 Introduction
2.2 Continuity of Derivations
2.3 Extension of Derivations
2.4 Hyperfinite von Neumann Algebras
2.5 Inner Derivations
2.6 Notes and Remarks
3. Averaging in Continuous and Normal Cohomology
3.1 Introduction
3.2 Averaging in Continuous Cohomology
3.3 Norm Continuous and Normal Cohomology are Equal: Extension Techniques
3.4 Averaging in Normal Cohomology
3.5 Notes and Remarks
4. Completely Bounded Cohomology
4.1 Introduction
4.2 Completely Bounded Cohomology into B(H)
4.3 Completely Bounded Cohomology into the Algebra
4.4 Notes and Remarks
5. Hyperfinite Subalgebras
5.1 Introduction
5.2 Extension by a Masa
5.3 Popa Subfactors and Masas
5.4 The Pisier-Haagerup-Grothendieck Inequality for Module Maps
5.5 Notes and Remarks
6. Continuous Cohomology
6.1 Introduction
6.2 Algebras Stable Under Tensor Products
6.3 Cohomology with Cartan Subalgebras
6.4 Cohomology for Factors with Property Γ
6.5 Separable Preduals
6.6 Notes and Remarks
7. Stability of Products
7.1 Introduction
7.2 Principal Component of the Automorphism Group
7.3 An Implicit Function Theorem
7.4 Stability
7.5 Notes and Remarks
8. Appendix
8.1 Introduction
8.2 Bounded Group Cohomology
8.3 Bounded Group Cohomology and Hochschild Cohomology
8.4 Problem List
Bibliography
A
Ch
Co
ER
Grot
J
KR
PhR
Ri
W
Notation
Index
Contents
Preface
0. Introduction
0.1 General Introduction
0.2 The Hochschild Complex
0.3 History
0.4 Averaging
0.5 Contents
0.6 Background
1. Completely Bounded Operators
1.1 Introduction
1.2 Completely Positive Maps
1.3 Completely Bounded Maps
1.4 The Haagerup Tensor Product
1.5 Multilinear Maps
1.6 Automatic Complete Boundedness
1.7 A Projection onto Completely Bounded Module Maps
1.8 Notes and Remarks
2. Derivations
2.1 Introduction
2.2 Continuity of Derivations
2.3 Extension of Derivations
2.4 Hyperfinite von Neumann Algebras
2.5 Inner Derivations
2.6 Notes and Remarks
3. Averaging in Continuous and Normal Cohomology
3.1 Introduction
3.2 Averaging in Continuous Cohomology
3.3 Norm Continuous and Normal Cohomology are Equal: Extension Techniques
3.4 Averaging in Normal Cohomology
3.5 Notes and Remarks
4. Completely Bounded Cohomology
4.1 Introduction
4.2 Completely Bounded Cohomology into B(H)
4.3 Completely Bounded Cohomology into the Algebra
4.4 Notes and Remarks
5. Hyperfinite Subalgebras
5.1 Introduction
5.2 Extension by a Masa
5.3 Popa Subfactors and Masas
5.4 The Pisier-Haagerup-Grothendieck Inequality for Module Maps
5.5 Notes and Remarks
6. Continuous Cohomology
6.1 Introduction
6.2 Algebras Stable Under Tensor Products
6.3 Cohomology with Cartan Subalgebras
6.4 Cohomology for Factors with Property Γ
6.5 Separable Preduals
6.6 Notes and Remarks
7. Stability of Products
7.1 Introduction
7.2 Principal Component of the Automorphism Group
7.3 An Implicit Function Theorem
7.4 Stability
7.5 Notes and Remarks
8. Appendix
8.1 Introduction
8.2 Bounded Group Cohomology
8.3 Bounded Group Cohomology and Hochschild Cohomology
8.4 Problem List
Bibliography
A
Ch
Co
ER
Grot
J
KR
PhR
Ri
W
Notation
Index
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