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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
DOI: https://doi.org/10.1090/S0002-9947-2014-06263-6
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
Email: echters@uni-muenster.de

Dana P. Williams
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
Email: dana.williams@Dartmouth.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06263-6
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.

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