scholarly journals Measures on Locally Compact Groups Whose Fourier-Stieltjes Transforms Vanish at Infinity and Group $C^*$-Algebras.

1994 ◽  
Vol 75 ◽  
pp. 115 ◽  
Author(s):  
Eberhard Kaniuth
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
C Algebras ◽  
Stieltjes Transforms

scholarly journals On $C*$-algebras associated with locally compact groups

1996 ◽  
Vol 124 (10) ◽  
pp. 3151-3158 ◽  
Author(s):  
M. B. Bekka ◽  
E. Kaniuth ◽  
A. T. Lau ◽  
G. Schlichting
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
C Algebras

scholarly journals APPROXIMATION PROPERTIES FOR CROSSED PRODUCTS BY ACTIONS AND COACTIONS

2001 ◽  
Vol 12 (05) ◽  
pp. 595-608 ◽  
Author(s):  
MAY M. NILSEN ◽  
ROGER R. SMITH
Keyword(s):  
Approximation Property ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Crossed Products ◽  
Approximation Properties ◽  
Locally Compact ◽  
Amenable Groups ◽  
C Algebras ◽  
Approximation Constant

We investigate approximation properties for C*-algebras and their crossed products by actions and coactions by locally compact groups. We show that Haagerup's approximation constant is preserved for crossed products by arbitrary amenable groups, and we show why this is not always true in the non-amenable case. We also examine similar questions for other forms of the approximation property.

Property T for general C*-algebras

2013 ◽  
Vol 156 (2) ◽  
pp. 229-239 ◽  
Author(s):  
CHI–KEUNG NG
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
C Algebras ◽  
Strong Property ◽  
Property T ◽  
Definition Of ◽  
Locally Compact Hausdorff Space

AbstractIn this paper, we extend the definition of property T and strong property T to general C*-algebras (not necessarily unital). We show that if an inclusion pair of locally compact groups (G,H) has property T, then (C*(G), C*(H)) has property T. As a partial converse, if T is abelian and C*(G) has property T, then T is compact. We also show that if Ω is a first countable locally compact Hausdorff space, then C0(Ω) has (strong) property T if and only if Ω is discrete. Furthermore, the non-unital C*-algebra $c_0(\mathbb{Z}^n)\rtimes SL_n(\mathbb{Z})$ has strong property T when n ≥ 3. We also give some equivalent forms of strong property T, which are new even in the unital case.

scholarly journals On the stable rank and real rank of group $C^*$-algebras of nilpotent locally compact groups

2005 ◽  
Vol 97 (1) ◽  
pp. 89
Author(s):  
Robert J. Archbold ◽  
Eberhard Kaniuth
Keyword(s):  
Abelian Group ◽  
Compact Group ◽  
Locally Compact Group ◽  
Stable Rank ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Real Rank ◽  
Locally Compact ◽  
C Algebras ◽  
Necessary And Sufficient

It is shown that if $G$ is an almost connected nilpotent group then the stable rank of $C^*(G)$ is equal to the rank of the abelian group $G/[G,G]$. For a general nilpotent locally compact group $G$, it is shown that finiteness of the rank of $G/[G,G]$ is necessary and sufficient for the finiteness of the stable rank of $C^*(G)$ and also for the finiteness of the real rank of $C^*(G)$.

scholarly journals A Duality of Locally Compact Groups That Does Not Involve the Haar Measure

2015 ◽  
Vol 116 (2) ◽  
pp. 250 ◽  
Author(s):  
Yulia Kuznetsova
Keyword(s):  
Compact Group ◽  
Haar Measure ◽  
Von Neumann Algebras ◽  
Locally Compact Group ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Von Neumann ◽  
C Algebras ◽  
Commutative Algebras

We present a simple and intuitive framework for duality of locally compacts groups, which is not based on the Haar measure. This is a map, functorial on a non-degenerate subcategory, on the category of coinvolutive Hopf $C^*$-algebras, and a similar map on the category of coinvolutive Hopf-von Neumann algebras. In the $C^*$-version, this functor sends $C_0(G)$ to $C^*(G)$ and vice versa, for every locally compact group $G$. As opposed to preceding approaches, there is an explicit description of commutative and co-commutative algebras in the range of this map (without assumption of being isomorphic to their bidual): these algebras have the form $C_0(G)$ or $C^*(G)$ respectively, where $G$ is a locally compact group. The von Neumann version of the functor puts into duality, in the group case, the enveloping von Neumann algebras of the algebras above: $C_0(G)^{**}$ and $C^*(G)^{**}$.

scholarly journals A higher category approach to twisted actions on c* -algebras

2012 ◽  
Vol 56 (2) ◽  
pp. 387-426 ◽  
Author(s):  
Alcides Buss ◽  
Ralf Meyer ◽  
Chenchang Zhu
Keyword(s):  
Classical Group ◽  
Group Actions ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Equivariant Maps ◽  
C Algebras ◽  
Covariant Representations ◽  
Group Case ◽  
Morita Equivalent

AbstractC*-algebras form a 2-category with *-homomorphisms or correspondences as morphisms and unitary intertwiners as 2-morphisms. We use this structure to define weak actions of 2-categories, weakly equivariant maps between weak actions and modifications between weakly equivariant maps. In the group case, we identify the resulting notions with known ones, including Busby–Smith twisted actions and the equivalence of such actions, covariant representations and saturated Fell bundles. For 2-groups, weak actions combine twists in the sense of Green, and Busby and Smith.The Packer–Raeburn Stabilization Trick implies that all Busby–Smith twisted group actions of locally compact groups are Morita equivalent to classical group actions. We generalize this to actions of strict 2-groupoids.

Twisted crossed products of C*-algebras

1989 ◽  
Vol 106 (2) ◽  
pp. 293-311 ◽  
Author(s):  
Judith A. Packer ◽  
Iain Raeburn
Keyword(s):  
Crossed Product ◽  
Group Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Crossed Products ◽  
Locally Compact ◽  
Basic Properties ◽  
C Algebras ◽  
General Family

Group algebras and crossed products have always played an important role in the theory of C*-algebras, and there has also been considerable interest in various twisted analogues, where the multiplication is twisted by a two-cocycle. Here we shall discuss a very general family of twisted actions of locally compact groups on C*-algebras, and the corresponding twisted crossed product C*-algebras. We shall then establish some of the basic properties of these algebras, motivated by the requirements of some applications we have in mind [2, 9, 10]. Some of our results will be known to others, at least in principle, but we feel that a coherent account might be useful.

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