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

Autores: Adam G. Skalski, Joachim Zacharias
Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 82, Nº 1, 2010, págs. 184-202
Idioma: inglés
DOI: 10.1112/jlms/jdq023
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Resumen
- 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.