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Permanence of approximation properties for discrete quantum groups (1407.3143v2)
Published 11 Jul 2014 in math.OA, math.GR, and math.QA
Abstract: We prove several results on the permanence of weak amenability and the Haagerup property for discrete quantum groups. In particular, we improve known facts on free products by allowing amalgamation over a finite quantum subgroup. We also define a notion of relative amenability for discrete quantum groups and link it with amenable equivalence of von Neumann algebras, giving additional permanence properties.