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

DOI:
https://doi.org/10.1090/S0002-9939-2013-11475-9

Published electronically:
February 1, 2013

MathSciNet review:
3020847

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Abstract | References | Similar Articles | Additional Information

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 -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

Email:
nadiasl@math.uio.no

**Xin Li**

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

Email:
xinli.math@uni-muenster.de

DOI:
https://doi.org/10.1090/S0002-9939-2013-11475-9

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.