Dilations of semigroup crossed products as crossed products of dilations
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- by Nadia S. Larsen and Xin Li PDF
- Proc. Amer. Math. Soc. 141 (2013), 1597-1603 Request permission
Abstract:
Laca constructed a minimal automorphic dilation for every semigroup dynamical system arising from an action of an Ore semigroup by injective endomorphisms of a unital $C^*$-algebra. Here we show that the semigroup crossed product with its action by inner endomorphisms given by the implementing isometries has as minimal automorphic dilation the group crossed product of the original dilation. Applications include recent examples studied by Cuntz and the second-named author.References
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Additional Information
- Nadia S. Larsen
- Affiliation: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway
- MR Author ID: 622552
- Email: nadiasl@math.uio.no
- Xin Li
- Affiliation: Department of Mathematics, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, 48149 Münster, Germany
- MR Author ID: 911893
- ORCID: 0000-0002-2243-3742
- Email: xinli.math@uni-muenster.de
- Received by editor(s): October 6, 2010
- Published electronically: February 1, 2013
- Additional Notes: The first-named author thanks J. Cuntz and S. Echterhoff for their kind hospitality during a sabbatical visit at Westfälische Wilhelms-Universität Münster in October 2009, where this research was initiated
The second-named author thanks the operator algebra group in Oslo for a nice visit at the University of Oslo.
This research was supported by the Research Council of Norway and the Deutsche Forschungsgemeinschaft - Communicated by: Marius Junge
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1597-1603
- MSC (2010): Primary 46L55
- DOI: https://doi.org/10.1090/S0002-9939-2013-11475-9
- MathSciNet review: 3020847