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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Authors: Siegfried Echterhoff and Dana P. Williams
Journal: Trans. Amer. Math. Soc. 366 (2014), 3649-3673
MSC (2010): Primary 46L55
Published electronically: March 4, 2014
MathSciNet review: 3192611
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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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Additional Information

Siegfried Echterhoff
Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62 D-48149 Münster, Germany
MR Author ID: 266728
ORCID: 0000-0001-9443-6451

Dana P. Williams
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
MR Author ID: 200378

Received by editor(s): August 21, 2012
Published electronically: March 4, 2014
Additional Notes: The research for this paper was partially supported by the German Research Foundation (SFB 478 and SFB 878) and the EU-Network Quantum Spaces Noncommutative Geometry (Contract No. HPRN-CT-2002-00280) as well as the Edward Shapiro Fund at Dartmouth College.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.