Abstract We study the Haagerup–Kraus approximation property for locally compact quantum
groups, generalising and unifying previous work by Kraus–Ruan and Crann. Along the way …

This is a survey of some aspects of the subject of approximation properties for locally
compact quantum groups, based on lectures given at the {\it Topological Quantum Groups} …

We prove that the orthogonal free quantum group factors L (FON) are strongly 1-bounded in
the sense of Jung. In particular, they are not isomorphic to free group factors. This result is …

We study Property (T) for locally compact quantum groups, providing several new
characterisations, especially related to operator algebraic ergodic theory. Quantum Property …

We study analogues of the radial subalgebras in free group factors (called the algebras of
class functions) in the setting of compact quantum groups. For the free orthogonal quantum …

Kazhdan's property (T) has been studied for several discrete group-like structures, including
standard invariants of Jones' subfactors and discrete quantum groups. We prove a Żuk-type …

We prove a number of property (T) permanence results for locally compact quantum groups
under exact sequences and the presence of invariant states, analogous to their classical …

Niech G b¦ dzie lokalnie zwart¡ 1 grup¡ abelow¡. Wraz z G mo» emy zwi¡ za¢ CG, zbiór
(mocno ci¡ gªych) reprezentacji nieprzywiedlnych. Wszystkie reprezentacje nieprzywiedlne …

Abstract For each λ∈] 0, 1] we exhibit an uncountable family of compact quantum groups G
such that the von Neumann algebra L∞(G) is the injective factor of type III λ with separable …

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 …