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Dilations of semigroup crossed products as crossed products of dilations

Authors: Nadia S. Larsen and Xin Li
Journal: Proc. Amer. Math. Soc. 141 (2013), 1597-1603
MSC (2010): Primary 46L55
Published electronically: February 1, 2013
MathSciNet review: 3020847
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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.

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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

Xin Li
Affiliation: Department of Mathematics, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, 48149 Münster, Germany

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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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