scholarly journals On reduced twisted group C*-algebras that are simple and/or have a unique trace

2018 ◽  
Vol 12 (3) ◽  
pp. 947-996 ◽  
Author(s):  
Erik Bédos ◽  
Tron Omland
Keyword(s):  
C Algebras ◽  
Twisted Group ◽  
Unique Trace

scholarly journals Fundamental Group of Simple C*-algebras with Unique Trace III

2012 ◽  
Vol 64 (3) ◽  
pp. 573-587 ◽  
Author(s):  
Norio Nawata
Keyword(s):  
Fundamental Group ◽  
Lower Semicontinuous ◽  
Classification Theorem ◽  
Fundamental Groups ◽  
C Algebras ◽  
Scalar Multiple ◽  
Unique Trace ◽  
Densely Defined

Abstract We introduce the fundamental group ℱ(A) of a simple σ-inital C*-algebra A with unique (up to scalar multiple) densely defined lower semicontinuous trace. This is a generalization of Fundamental Group of Simple C*-algebras with Unique Trace I and II by Nawata andWatatani. Our definition in this paper makes sense for stably projectionless C*-algebras. We show that there exist separable stably projectionless C*-algebras such that their fundamental groups are equal to ℝ×+ by using the classification theorem of Razak and Tsang. This is a contrast to the unital case in Nawata and Watatani. This study is motivated by the work of Kishimoto and Kumjian.

scholarly journals Homogeneous C*-algebras whose spectra are tori

1985 ◽  
Vol 38 (1) ◽  
pp. 9-39 ◽  
Author(s):  
Shaun Disney ◽  
Iain Raeburn
Keyword(s):  
Isomorphism Class ◽  
Homotopy Theory ◽  
Transformation Group ◽  
Crossed Products ◽  
C Algebras ◽  
Isomorphism Classes ◽  
Twisted Group

AbstractBy a theorem of Fell and Tomiyama-Takesaki, an N-homogeneous C*-algebra with spectrum X has the form Γ(E) for some bundle E over X with fibre MN(C), and its isomorphism class is determined by that of E and its pull-backs f*E along homeomorphisms f of X. We describe the homogeneous C*-algebras with spectrum T2 or T3 by classifying the MN-bundles over Tk using elementary homotopy theory. We then use our results to determine the isomorphism classes of a variety of transformation group C*-algebras, twisted group C*-algebras and more general crossed products.

scholarly journals On the Structure of Twisted Group C ∗ -Algebras

1992 ◽  
Vol 334 (2) ◽  
pp. 685 ◽  
Author(s):  
Judith A. Packer ◽  
Iain Raeburn
Keyword(s):  
C Algebras ◽  
Twisted Group

scholarly journals Gabor duality theory for Morita equivalent C∗-algebras

2020 ◽  
Vol 31 (10) ◽  
pp. 2050073 ◽  
Author(s):  
Are Austad ◽  
Mads S. Jakobsen ◽  
Franz Luef
Keyword(s):  
Duality Theory ◽  
Morita Equivalence ◽  
Gabor Frames ◽  
Duality Principle ◽  
Gabor Analysis ◽  
Matrix Algebras ◽  
C Algebras ◽  
Morita Equivalent ◽  
Twisted Group ◽  
Density Theorems

The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalence bimodules with some extra properties. For certain twisted group [Formula: see text]-algebras, the reformulation of the duality principle to the setting of Morita equivalence bimodules reduces to the well-known Gabor duality principle by localizing with respect to a trace. We may lift all results at the module level to matrix algebras and matrix modules, and in doing so, it is natural to introduce [Formula: see text]-matrix Gabor frames, which generalize multi-window super Gabor frames. We are also able to establish density theorems for module frames on equivalence bimodules, and these localize to density theorems for [Formula: see text]-matrix Gabor frames.

Twisted Group C*-Algebras as Compact Quantum Metric Spaces

2016 ◽  
Vol 71 (3-4) ◽  
pp. 911-931 ◽  
Author(s):  
Botao Long ◽  
Wei Wu
Keyword(s):  
Metric Spaces ◽  
C Algebras ◽  
Twisted Group

A class of groups producing simple, unique trace C*-algebras

1993 ◽  
Vol 114 (2) ◽  
pp. 223-233 ◽  
Author(s):  
S. David Promislow
Keyword(s):  
Open Problems ◽  
C Algebras ◽  
Unique Trace

AbstractWe define and study a class of groups which produce simple, unique trace, C*-algebras. This class strictly contains the class of weak Powers groups, as shown by the fact that it is closed under extensions. We provide answers to some open problems involving Powers and weak Powers groups.

scholarly journals Primeness and Primitivity Conditions for Twisted Group $C^*$-Algebras

2014 ◽  
Vol 114 (2) ◽  
pp. 299 ◽  
Author(s):  
Tron Ånen Omland
Keyword(s):  
Discrete Group ◽  
Direct Products ◽  
Free Products ◽  
C Algebra ◽  
C Algebras ◽  
Twisted Group ◽  
Products Of Groups

For a multiplier (2-cocycle) $\sigma$ on a discrete group $G$ we give conditions for which the twisted group $C^*$-algebra associated with the pair $(G,\sigma)$ is prime or primitive. We also discuss how these conditions behave on direct products and free products of groups.

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