Operator Algebras (eBook)

Preface to the Series 6
Preface 7
Contents 9
Interpolation by Projections in C*-Algebras 11
1 Introduction 11
2 Main Results 14
3 Some Applications 18
References 22
KMS States and Complex Multiplication ( Part II*) 24
1 Introduction 24
2 Quantum Statistical Mechanics and Explicit Class Field Theory 28
3 Q-lattices and Noncommutative Shimura Varieties 33
4 Quantum Statistical Mechanics for Imaginary Quadratic Fields 53
5 KMS States and Complex Multiplication 62
References 67
An Algebraic Description of Boundary Maps Used in Index Theory 69
1 Boundary Maps and Bott Maps 71
2 The Categories kkalg and kk 80
3 Abstract Kasparov Modules 81
4 The Boundary Map in the Baum-Douglas Situation 85
5 The Case of C*-Algebras 90
6 The Index Theorem of Baum-Douglas-Taylor 91
References 93
On Rørdam’s Classification of Certain Algebras with One Non-Trivial Ideal 95
1 Introduction 95
2 Bonkat’s Method 96
3 Unital Classification 99
References 103
Perturbation of Hausdorff Moment Sequences, and an Application to the Theory of C*-Algebras of Real Rank Zero 105
1 Introduction 105
2 Initial Objects in Unital Real Rank Zero C*-Algebras 107
3 Simple Initial Objects 109
4 Hausdorff Moments, the GICAR-Algebra, and Pascal’s Triangle 114
5 Properties of Initial Objects 120
References 123
Twisted K-Theory and Modular Invariants: I Quantum Doubles of Finite Groups 124
1 Introduction and Statement of Results 124
2 Twisted Quantum Doubles of Finite Groups 127
3 Twisted Equivariant Bundles over Finite Groups 138
4 Examples 142
References 149
The Orbit Structure of Cantor Minimal Z2- Systems 152
1 Introduction 152
2 Étale Equivalence Relations 153
3 Invariants for Cantor Étale Equivalence Relation 155
4 AF-Equivalence Relations 156
5 The Classification of AF-Equivalence Relations 157
6 The Strategy for Orbit Equivalence Results 158
7 The Absorption Theorem 159
8 Classification up to Orbit Equivalence of Minimal Z- Actions 159
9 Classification up to Orbit Equivalence of Minimal Z2- Actions 161
10 Further Developments 165
References 166
Outer Actions of a Group on a Factor 168
References 170
Non-Separable AF-Algebras 171
1 Introduction 171
2 Proof of Theorem 6 174
3 A Prime AF-Algebra Which is Not Primitive 177
References 179
Central Sequences in C*-Algebras and Strongly Purely Infinite Algebras 180
1 Introduction: The Stable Invariant 180
2 The Case of Simple 188
3 The Invariant cov(F(A)) and Applications 201
4 Self-Absorbing Subalgebras of 208
A Elementary Properties of Ultrapowers. 221
B Proofs of Results in Section 1 224
C Some Calculations with KTP 232
References 234
Lifting of an Asymptotically Inner Flow for a Separable C*-Algebra 237
1 Introduction 237
2 Asymptotically Inner Flows 239
3 Lifting 244
References 251
Remarks on Free Entropy Dimension 252
Introduction 252
1 Unbounded Dual Systems and Derivations 253
2 Dual Systems and L2 Cohomology 255
3 Some Remarks on Semi-Continuity of Free Dimension 258
References 260
Notes on Treeability and Costs for Discrete Groupoids in Operator Algebra Framework 261
1 Introduction 261
2 A Criterion for Treeability 262
3 Operator Algebra Approach to Gaboriau’s Results 269
References 280