Structure of crossed products by strictly proper actions on continuous-trace algebras

Echterhoff, Siegfried; Williams, Dana

doi:10.1090/S0002-9947-2014-06263-6

Structure of crossed products by strictly proper actions on continuous-trace algebras
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by Siegfried Echterhoff and Dana P. Williams PDF

Trans. Amer. Math. Soc. 366 (2014), 3649-3673 Request permission

Abstract:

We examine the ideal structure of crossed products $B\rtimes _{\beta }G$ where $B$ is a continuous-trace $C^*$-algebra and the induced action of $G$ on the spectrum of $B$ is proper. In particular, we are able to obtain a concrete description of the topology on the spectrum of the crossed product in the cases where either $G$ is discrete or $G$ is a Lie group acting smoothly on the spectrum of $B$.

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