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Strongly self-absorbing $ \mathrm{C}^*$-dynamical systems


Author: Gábor Szabó
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 46L55
DOI: https://doi.org/10.1090/tran/6931
Published electronically: July 13, 2017
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Abstract: We introduce and study strongly self-absorbing actions of locally compact groups on $ \mathrm {C}^*$-algebras. This is an equivariant generalization of a strongly self-absorbing $ \mathrm {C}^*$-algebra to the setting of $ \mathrm {C}^*$-dynamical systems. The main result is the following equivariant McDuff-type absorption theorem: A cocycle action $ (\alpha ,u): G\curvearrowright A$ on a separable $ \mathrm {C}^*$-algebra is cocycle conjugate to its tensorial stabilization with a strongly self-absorbing action $ \gamma : G\curvearrowright \mathcal {D}$, if and only if there exists an equivariant and unital $ *$-homomorphism from $ \mathcal {D}$ into the central sequence algebra of $ A$. We also discuss some non-trivial examples of strongly self-absorbing actions.


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Additional Information

Gábor Szabó
Affiliation: Fachbereich Mathematik, Westfälische Wilhelms-Universität, Einsteinstrasse 62, 48149 Münster, Germany
Address at time of publication: Institute of Mathematics, Fraser Noble Building, University of Aberdeen, Aberdeen AB24 3UE, Scotland, United Kingdom
Email: gabor.szabo@abdn.ac.uk

DOI: https://doi.org/10.1090/tran/6931
Received by editor(s): September 29, 2015
Received by editor(s) in revised form: March 8, 2016
Published electronically: July 13, 2017
Additional Notes: The author was supported by SFB 878 Groups, Geometry and Actions
Article copyright: © Copyright 2017 American Mathematical Society