Bratteli / Neshveyev / Skau Operator Algebras

The Abel Symposium 2004
1. Auflage 2007
ISBN: 978-3-540-34197-0
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 279 Seiten

The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as 'non-commutative geometry'. It has branched out in several sub-disciplines and made contact with other subjects. The contributions to this volume give a state-of-the-art account of some of these sub-disciplines and the variety of topics reflect to some extent how the subject has developed. This is the first volume in a prestigious new book series linked to the Abel prize.

Autoren/Hrsg.

Bratteli, Ola

Neshveyev, Sergey

Skau, Christian

Inhaltsverzeichnis

1;Preface to the Series;6
2;Preface;7
3;Contents;9
4;Interpolation by Projections in C*-Algebras;11
4.1;1 Introduction;11
4.2;2 Main Results;14
4.3;3 Some Applications;18
4.4;References;22
5;KMS States and Complex Multiplication ( Part II*);24
5.1;1 Introduction;24
5.2;2 Quantum Statistical Mechanics and Explicit Class Field Theory;28
5.3;3 Q-lattices and Noncommutative Shimura Varieties;33
5.4;4 Quantum Statistical Mechanics for Imaginary Quadratic Fields;53
5.5;5 KMS States and Complex Multiplication;62
5.6;References;67
6;An Algebraic Description of Boundary Maps Used in Index Theory;69
6.1;1 Boundary Maps and Bott Maps;71
6.2;2 The Categories kkalg and kk;80
6.3;3 Abstract Kasparov Modules;81
6.4;4 The Boundary Map in the Baum-Douglas Situation;85
6.5;5 The Case of C*-Algebras;90
6.6;6 The Index Theorem of Baum-Douglas-Taylor;91
6.7;References;93
7;On Rørdam’s Classification of Certain Algebras with One Non-Trivial Ideal;95
7.1;1 Introduction;95
7.2;2 Bonkat’s Method;96
7.3;3 Unital Classification;99
7.4;References;103
8;Perturbation of Hausdorff Moment Sequences, and an Application to the Theory of C*-Algebras of Real Rank Zero;105
8.1;1 Introduction;105
8.2;2 Initial Objects in Unital Real Rank Zero C*-Algebras;107
8.3;3 Simple Initial Objects;109
8.4;4 Hausdorff Moments, the GICAR-Algebra, and Pascal’s Triangle;114
8.5;5 Properties of Initial Objects;120
8.6;References;123
9;Twisted K-Theory and Modular Invariants: I Quantum Doubles of Finite Groups;124
9.1;1 Introduction and Statement of Results;124
9.2;2 Twisted Quantum Doubles of Finite Groups;127
9.3;3 Twisted Equivariant Bundles over Finite Groups;138
9.4;4 Examples;142
9.5;References;149
10;The Orbit Structure of Cantor Minimal Z2- Systems;152
10.1;1 Introduction;152
10.2;2 Étale Equivalence Relations;153
10.3;3 Invariants for Cantor Étale Equivalence Relation;155
10.4;4 AF-Equivalence Relations;156
10.5;5 The Classification of AF-Equivalence Relations;157
10.6;6 The Strategy for Orbit Equivalence Results;158
10.7;7 The Absorption Theorem;159
10.8;8 Classification up to Orbit Equivalence of Minimal Z- Actions;159
10.9;9 Classification up to Orbit Equivalence of Minimal Z2- Actions;161
10.10;10 Further Developments;165
10.11;References;166
11;Outer Actions of a Group on a Factor;168
11.1;References;170
12;Non-Separable AF-Algebras;171
12.1;1 Introduction;171
12.2;2 Proof of Theorem 6;174
12.3;3 A Prime AF-Algebra Which is Not Primitive;177
12.4;References;179
13;Central Sequences in C*-Algebras and Strongly Purely Infinite Algebras;180
13.1;1 Introduction: The Stable Invariant;180
13.2;2 The Case of Simple;188
13.3;3 The Invariant cov(F(A)) and Applications;201
13.4;4 Self-Absorbing Subalgebras of;208
13.5;A Elementary Properties of Ultrapowers.;221
13.6;B Proofs of Results in Section 1;224
13.7;C Some Calculations with KTP;232
13.8;References;234
14;Lifting of an Asymptotically Inner Flow for a Separable C*-Algebra;237
14.1;1 Introduction;237
14.2;2 Asymptotically Inner Flows;239
14.3;3 Lifting;244
14.4;References;251
15;Remarks on Free Entropy Dimension;252
15.1;Introduction;252
15.2;1 Unbounded Dual Systems and Derivations;253
15.3;2 Dual Systems and L2 Cohomology;255
15.4;3 Some Remarks on Semi-Continuity of Free Dimension;258
15.5;References;260
16;Notes on Treeability and Costs for Discrete Groupoids in Operator Algebra Framework;261
16.1;1 Introduction;261
16.2;2 A Criterion for Treeability;262
16.3;3 Operator Algebra Approach to Gaboriau’s Results;269
16.4;References;280