Crossed products of continuous-trace 𝐶*-algebras by smooth actions

Raeburn, Iain; Rosenberg, Jonathan

doi:10.1090/S0002-9947-1988-0920145-6

Crossed products of continuous-trace $C^ \ast$-algebras by smooth actions
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by Iain Raeburn and Jonathan Rosenberg

Trans. Amer. Math. Soc. 305 (1988), 1-45

DOI: https://doi.org/10.1090/S0002-9947-1988-0920145-6

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Abstract:

We study in detail the structure of ${C^{\ast }}$-crossed products of the form $A \rtimes {}_\alpha G$, where $A$ is a continuous-trace algebra and $\alpha$ is an action of a locally compact abelian group $G$ on $A$, especially in the case where the action of $G$ on $\hat A$ has a Hausdorff quotient and only one orbit type. Under mild conditions, the crossed product has continuous trace, and we are often able to compute its spectrum and Dixmier-Douady class. The formulae for these are remarkably interesting even when $G$ is the real line.

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