On 𝐶*-algebras associated with locally compact groups

Abstract

Let G G be a locally compact group, and let G d G_{d} denote the same group G G with the discrete topology. There are various C ∗ -algebras C^{*}\text {-algebras} associated to G G and G d . G_{d}. We are concerned with the question of when these C ∗ -algebras 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.