Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups

Skalski, A. and Zacharias, J. (2010) Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups. Journal of the London Mathematical Society, 82(1), pp. 184-202. (doi:10.1112/jlms/jdq023)

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Publisher's URL: http://dx.doi.org/10.1112/jlms/jdq023

Abstract

We construct explicit approximating nets for crossed products of C*-algebras by actions of discrete quantum groups. This implies that C*-algebraic approximation properties such as nuclearity, exactness or completely bounded approximation are preserved by taking crossed products by the actions of amenable discrete quantum groups. We also show that the noncommutative topological entropy of a transformation commuting with the quantum group action does not change when we pass to the canonical extension to the crossed product. Both these results are extended to twisted crossed products via a stabilization trick.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Zacharias, Dr Joachim
Authors: Skalski, A., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of the London Mathematical Society
Journal Abbr.:J. London Math. Soc.
ISSN:0024-6107
ISSN (Online):1469-7750
Published Online:28 June 2010

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