Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups
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 property are preserved by taking crossed products by 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 stabilisation trick.
Keywords
Cite
@article{arxiv.0807.2827,
title = {Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups},
author = {Adam Skalski and Joachim Zacharias},
journal= {arXiv preprint arXiv:0807.2827},
year = {2014}
}
Comments
20 pages, v4 fixes a few typos and expands some parts of the presentation. The final version of the paper will appear in the Journal of the London Mathematical Society