The notion of an open quantum subgroup of a locally compact quantum group is introduced
and given several equivalent characterizations in terms of group-like projections, inclusions …

Given a quantum permutation group G⊂ SN+, with orbits having the same size K, we
construct a universal matrix model π: C (G)→ MK (C (X)), having the property that the images …

We classify all compact quantum groups whose C*-algebra sits inside that of the free unitary
quantum groups $ U_ {N}^{+} $. In other words, we classify all discrete quantum subgroups …

This book introduces the reader to quantum groups, focusing on the simplest ones, namely
the closed subgroups of the free unitary group. Although such quantum groups are quite …

The notion of normal quantum subgroup introduced in algebraic context by Parshall and
Wang when applied to compact quantum groups is shown to be equivalent to the notion of …

To any action of a compact quantum group on a von Neumann algebra which is a direct sum
of factors we associate an equivalence relation corresponding to the partition of a space into …

Associated to any compact quantum group $ G\subset U_ {N}^{+} $ is a canonical family of
group dual subgroups $\widehat {\Gamma} _ {Q}\subset G $, parametrized by unitaries …

We introduce a class of automorphisms of compact quantum groups (CQGs) which may be
thought of as inner automorphisms and explore the behavior of normal subgroups of CQGs …

We prove a number of results linking properties of actions by compact groups (both quantum
and classical) on Banach spaces, such as uniform continuity, spectrum finiteness and …

This paper initiates the study of non‐commutative dynamical systems of the form (G, Γ),
where a discrete group Γ acts on a compact quantum group (CQG) G by quantum …