ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Operator Algebras The Abel Symposium 2004

:	Ola Bratteli, Sergey Neshveyev, Christian Skau
:	Ola Bratteli, Sergey Neshveyev, Christian Skau
:	Operator Algebras The Abel Symposium 2004
:	Springer-Verlag
:	9783540341970
:	1
:	CHF 85.60
:

:	Analysis
:	English

:	279
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

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.

	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