scholarly journals SOFT C*-ALGEBRAS

2002 ◽  
Vol 45 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Carla Farsi
Keyword(s):  
Stable Rank ◽  
Crossed Product ◽  
Subject Classification ◽  
Large Classes ◽  
C Algebras ◽  
Primary 46L80

AbstractIn this paper we consider soft group and crossed product $C^*$-algebras. In particular we show that soft crossed product $C^*$-algebras are isomorphic to classical crossed product $C^*$-algebras. We also prove that large classes of soft $C^*$-algebras have stable rank equal to infinity.AMS 2000 Mathematics subject classification: Primary 46L80; 46L55

scholarly journals C*-algebras of a Cantor system with finitely many minimal subsets: structures, K-theories, and the index map

2020 ◽  
pp. 1-46 ◽  
Author(s):  
SERGEY BEZUGLYI ◽  
ZHUANG NIU ◽  
WEI SUN
Keyword(s):  
Directed Graphs ◽  
Cantor Set ◽  
Stable Rank ◽  
Crossed Product ◽  
Real Rank ◽  
C Algebra ◽  
C Algebras ◽  
Rank 2 ◽  
Stably Finite ◽  
The Ideal

We study homeomorphisms of a Cantor set with $k$ ( $k<+\infty$ ) minimal invariant closed (but not open) subsets; we also study crossed product C*-algebras associated to these Cantor systems and certain of their orbit-cut sub-C*-algebras. In the case where $k\geq 2$ , the crossed product C*-algebra is stably finite, has stable rank 2, and has real rank 0 if in addition $(X,\unicode[STIX]{x1D70E})$ is aperiodic. The image of the index map is connected to certain directed graphs arising from the Bratteli–Vershik–Kakutani model of the Cantor system. Using this, it is shown that the ideal of the Bratteli diagram (of the Bratteli–Vershik–Kakutani model) must have at least $k$ vertices at each level, and the image of the index map must consist of infinitesimals.

scholarly journals Classifying crossed product C*-algebras

2016 ◽  
Vol 138 (3) ◽  
pp. 793-820 ◽  
Author(s):  
Wilhelm Winter
Keyword(s):  
Crossed Product ◽  
C Algebras

scholarly journals A NON-EXTENDABLE BOUNDED LINEAR MAP BETWEEN C*-ALGEBRAS

2001 ◽  
Vol 44 (2) ◽  
pp. 241-248 ◽  
Author(s):  
Narutaka Ozawa
Keyword(s):  
Linear Extension ◽  
Subject Classification ◽  
Primary 46L05 ◽  
Bounded Linear ◽  
Linear Map ◽  
C Algebras ◽  
Secondary 46L07

AbstractWe present an example of a $C^*$-subalgebra $A$ of $\mathbb{B}(H)$ and a bounded linear map from $A$ to $\mathbb{B}(K)$ which does not admit any bounded linear extension. This generalizes the result of Robertson and gives the answer to a problem raised by Pisier. Using the same idea, we compute the exactness constants of some Q-spaces. This solves a problem raised by Oikhberg. We also construct a Q-space which is not locally reflexive.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 46L07

scholarly journals ON THE CLASSIFICATION OF NUCLEAR C*-ALGEBRAS

2002 ◽  
Vol 85 (1) ◽  
pp. 168-210 ◽  
Author(s):  
MARIUS DADARLAT ◽  
SØREN EILERS
Keyword(s):  
Subject Classification ◽  
Unified Approach ◽  
C Algebras ◽  
Starting Point ◽  
K Theory

We employ results from KK-theory, along with quasidiagonality techniques, to obtain wide-ranging classification results for nuclear C*-algebras. Using a new realization of the Cuntz picture of the Kasparov groups we show that two morphisms inducing equal KK-elements are approximately stably unitarily equivalent. Using K-theory with coefficients to associate a partial KK-element to an approximate morphism, our result is generalized to cover such maps. Conversely, we study the problem of lifting a (positive) partial KK-element to an approximate morphism. These results are employed to obtain classification results for certain classes of quasidiagonal C*-algebras introduced by H. Lin, and to reprove the classification of purely infinite simple nuclear C*-algebras of Kirchberg and Phillips. It is our hope that this work can be the starting point of a unified approach to the classification of nuclear C*-algebras.2000 Mathematical Subject Classification: primary 46L35; secondary 19K14, 19K35, 46L80.

CROSSED PRODUCT C*-ALGEBRAS AND ALGEBRAIC TOPOLOGY

1996 ◽  
Vol 08 (04) ◽  
pp. 623-637
Author(s):  
JUDITH A. PACKER
Keyword(s):  
Algebraic Topology ◽  
Equivariant Cohomology ◽  
Automorphism Groups ◽  
Crossed Product ◽  
Fiber Bundles ◽  
Topological Invariants ◽  
C Algebras ◽  
Recent Developments ◽  
Continuous Trace ◽  
Cech Cohomology

We discuss some recent developments that illustrate the interplay between the theory of crossed products of continuous trace C*-algebras and algebraic topology, summarizing results relating topological invariants coming from the theory of fiber bundles to continuous trace C*-algebras and their automorphism groups and the structure of the associated crossed product C*-algebras. This survey article starts from the classical theory of Dixmier, Douady, and Fell, and discusses the more recent work of Echterhoff, Phillips, Raeburn, Rosenberg, and Williams, among others. The topological invariants involved are Čech cohomology, the cohomology of locally compact groups with Borel cochains of C. Moore, and the recently introduced equivariant cohomology theory of Crocker, Kumjian, Raeburn and Williams.

scholarly journals Extension problems and non-Abelian duality for C*-algebras

2007 ◽  
Vol 75 (2) ◽  
pp. 229-238 ◽  
Author(s):  
Astrid an Huef ◽  
S. Kaliszewski ◽  
Iain Raeburn
Keyword(s):  
Compact Group ◽  
Unitary Representation ◽  
Closed Subgroup ◽  
Locally Compact Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Test Question ◽  
Locally Compact ◽  
Dual Representation ◽  
C Algebras

Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

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