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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Crossed products of continuous-trace $ C\sp \ast$-algebras by smooth actions


Authors: Iain Raeburn and Jonathan Rosenberg
Journal: Trans. Amer. Math. Soc. 305 (1988), 1-45
MSC: Primary 46L55; Secondary 22D25, 46L40, 46M20
MathSciNet review: 920145
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0920145-6
PII: S 0002-9947(1988)0920145-6
Article copyright: © Copyright 1988 American Mathematical Society