On 𝐶*-algebras associated with locally compact groups

Bekka, M.; Kaniuth, E.; Lau, A.; Schlichting, G.

doi:10.1090/S0002-9939-96-03382-5

On $C*$-algebras associated with locally compact groups
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by M. B. Bekka, E. Kaniuth, A. T. Lau and G. Schlichting PDF

Proc. Amer. Math. Soc. 124 (1996), 3151-3158 Request permission

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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