On transformation group 𝐶*-algebras with continuous trace

Echterhoff, Siegfried

doi:10.1090/S0002-9947-1994-1157612-1

On transformation group $C^ *$-algebras with continuous trace
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Trans. Amer. Math. Soc. 343 (1994), 117-133 Request permission

Abstract:

In this paper we answer some questions posed by Dana Williams in [19] concerning the problem under which conditions the transformation group ${C^ \ast }$-algebra ${C^\ast }(G,\Omega )$ of a locally compact transformation group (G, $\Omega$) has continuous trace. One consequence will be, for compact G, that ${C^\ast }(G,\Omega )$ has continuous trace if and only if the stabilizer map is continuous. We also give a complete solution to the problem if G is discrete.

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