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Publication
Actions of Monoidally Equivalent Compact Quantum Groups and Applications to Probabilistic Boundaries
Journal Contribution - Journal Article
Abstract:The notion of monoidal equivalence for compact quantum groups
was recently introduced by Bichon, De Rijdt and Vaes. 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.
This correspondence turns out to be very useful to obtain the behavior of Poisson
and Martin boundaries under monoidal equivalence of quantum groups. Finally,
we apply these results to identify the Poisson boundary for the duals of quantum
automorphism groups.
was recently introduced by Bichon, De Rijdt and Vaes. 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.
This correspondence turns out to be very useful to obtain the behavior of Poisson
and Martin boundaries under monoidal equivalence of quantum groups. Finally,
we apply these results to identify the Poisson boundary for the duals of quantum
automorphism groups.
Published in: Annales de l'Institut Fourier
ISSN: 0373-0956
Issue: 1
Volume: 60
Pages: 169-216
Publication year:2010
Keywords:Pure mathematics
Review status:Peer-reviewed