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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On $C^{*}$-algebras associated
with locally compact groups


Authors: M. B. Bekka, E. Kaniuth, A. T. Lau and G. Schlichting
Journal: Proc. Amer. Math. Soc. 124 (1996), 3151-3158
MSC (1991): Primary 43A30, 22D10
MathSciNet review: 1328338
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Abstract: Let $G$ be a locally compact group, and let $G_{d}$ denote the same group $G$ with the discrete topology. There are various $C^{*}\text {-algebras}$ associated to $G$ and $G_{d}.$ We are concerned with the question of when these $C^{*}\text {-algebras}$ are isomorphic. This is intimately related to amenability. The results can be reformulated in terms of Fourier and Fourier-Stieltjes algebras and of weak containment properties of unitary representations.


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Additional Information

M. B. Bekka
Affiliation: Département de Mathématiques, University de Metz, UFR M.I.M. Ile du Saulcy, F-57045 Metz Cedex 01, France
Email: bekka@poncelet.univ-metz.fr

E. Kaniuth
Affiliation: Fachbereich Mathematik-Informatik, Universität-GH Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
Email: kaniuth@uni-paderborn.de

A. T. Lau
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: tlau@vega.math.ualberta.ca

G. Schlichting
Affiliation: Mathematisches Institut, Technische Universität München, Arcisstrasse 21, W-80333 München 2, Germany
Email: gschlich@mathematik.tu-muenchen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03382-5
PII: S 0002-9939(96)03382-5
Keywords: Amenable group, connected Lie group, group $C^{*}$-algebra, weak containment, Fourier algebra
Additional Notes: This research is supported by a NATO collaborative research grant 940184.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society