49 citations · 198 across the 15 of their papers we have counts for
15 papers · 1 filter
-simplicity and boundary actions of discrete quantum groups
Benjamin Anderson-Sackaney, Roland Vergnioux
We introduce and investigate several quantum group dynamical notions for the purpose of studying -simplicity of discrete quantum groups via the theory of boundary actions. In…
Maximal amenability of the radial subalgebra in free quantum group factors
Roland Vergnioux, Xumin Wang
We show that the radial MASA in the orthogonal free quantum group algebra L(FO_N) is maximal amenable if N is large enough, using the Asymptotic Orthogonality Property. This relies…
K-amenability for amalgamated free products of amenable discrete quantum groups
Roland Vergnioux
The basic notions and results of equivariant KK-theory concerning crossed products can be extended to the case of locally compact quantum groups. We recall these constructions and…
The Property of Rapid Decay for Discrete Quantum Groups
Roland Vergnioux
We introduce the Property of Rapid Decay for discrete quantum groups by equivalent characterizations that generalize the classical ones. We then investigate examples, proving in pa…
Orientation of quantum Cayley trees and applications
Roland Vergnioux
We introduce the quantum Cayley graphs associated to quantum discrete groups and study them in the case of trees. We focus in particular on the notion of quantum ascending orientat…
Noncommutative Furstenberg boundary
Mehrdad Kalantar, Paweł Kasprzak, Adam Skalski +1
We introduce and study the notions of boundary actions and of the Furstenberg boundary of a discrete quantum group. As for classical groups, properties of boundary actions turn out…