Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

Details Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

2006-11-07

arxiv.org/abs/math/0611175v3

Mathematics

Operator Algebras

31 pages

Scientific paper

Bichon, De Rijdt and Vaes introduced the notion of monoidally equivalent compact quantum groups. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital C*-algebras or on von Neumann algebras. We apply this correspondence to study the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups.

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