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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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
  • Email: echters@uni-muenster.de
  • Dana P. Williams
  • Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
  • MR Author ID: 200378
  • Email: dana.williams@Dartmouth.edu
  • 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.
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3649-3673
  • MSC (2010): Primary 46L55
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06263-6
  • MathSciNet review: 3192611