On the Baum--Connes conjecture for discrete quantum groups with torsion and the quantum Rosenberg Conjecture

Autor:	Arano, Yuki, Skalski, Adam
Rok vydání:	2020
Předmět:	Mathematics - Operator Algebras Primary 46L67 Secondary 46L80
Druh dokumentu:	Working Paper
Popis:	We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsions. As an outcome, we show that the crossed product by a discrete quantum group in a certain class preserves the UCT. We then show that quasidiagonality of a reduced C*-algebra of a countable discrete quantum group $\Gamma$ implies that $\Gamma$ is amenable, and deduce from the work of Tikuisis, White and Winter, and the results in the first part of the paper, the converse (i.e. the quantum Rosenberg Conjecture) for a large class of countable discrete unimodular quantum groups. We also note that the unimodularity is a necessary condition. Comment: 15 pages, v2 corrects a few minor points. The final version of the paper will appear in the Proceedings of the American Mathematical Society
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.12453 Zobrazit plný text záznamu View this record from Arxiv