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

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

2008-07-17

arxiv.org/abs/0807.2827v4

Mathematics

Operator Algebras

20 pages, v4 fixes a few typos and expands some parts of the presentation. The final version of the paper will appear in the J

Scientific paper

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.

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