Dilations of semigroup crossed products as crossed products of dilations
Authors:
Nadia S. Larsen and Xin Li
Journal:
Proc. Amer. Math. Soc. 141 (2013), 15971603
MSC (2010):
Primary 46L55
Published electronically:
February 1, 2013
MathSciNet review:
3020847
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Abstract 
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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 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 secondnamed author.
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Additional Information
Nadia S. Larsen
Affiliation:
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N0316 Oslo, Norway
Email:
nadiasl@math.uio.no
Xin Li
Affiliation:
Department of Mathematics, Westfälische WilhelmsUniversität Münster, Einsteinstraße 62, 48149 Münster, Germany
Email:
xinli.math@unimuenster.de
DOI:
http://dx.doi.org/10.1090/S000299392013114759
PII:
S 00029939(2013)114759
Received by editor(s):
October 6, 2010
Published electronically:
February 1, 2013
Additional Notes:
The firstnamed author thanks J. Cuntz and S. Echterhoff for their kind hospitality during a sabbatical visit at Westfälische WilhelmsUniversität Münster in October 2009, where this research was initiated
The secondnamed 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.
