72 citations · 212 across the 16 of their papers we have counts for
16 papers
Braided tensor product of von Neumann algebras
Kenny De Commer, Jacek Krajczok
We introduce a definition of braided tensor product of von Neumann algebras equipped with an action of a quasi-triangular qua…
Representation theory of the Reflection Equation Algebra II: Theory of shapes
Kenny De Commer, Stephen T. Moore
We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the -matrix associated to th…
Partial -algebraic quantum groups and Drinfeld doubles of partial compact quantum groups
Kenny De Commer, Johan Konings
We introduce a notion of partial algebraic quantum group. This is an important special case of a weak multiplier Hopf algebra with integrals, as introduced in the work of Van Daele…
Projective representation theory for compact quantum groups and the quantum Baum-Connes assembly map
Kenny De Commer, Rubén Martos, Ryszard Nest
We study the theory of projective representations for a compact quantum group , i.e. actions of on for some Hilbert space . We show tha…
Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik-Zamolodchikov equations and Letzter-Kolb coideals
Kenny De Commer, Sergey Neshveyev, Lars Tuset +1
We establish an equivalence between two approaches to quantization of irreducible symmetric spaces of compact type within the framework of quasi-coactions, one based on the Enrique…
Quantum actions on discrete quantum spaces and a generalization of Clifford's theory of representations
Kenny De Commer, Paweł Kasprzak, Adam Skalski +1
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 in…
A field of quantum upper triangular matrices
K. De Commer, M. Floré
We show that the duals of Woronowicz's quantum SU(2)-groups converge, within the operator algebraic setting, to the group of special upper triangular 2-by-2 matrices with positive…
Partial compact quantum groups
Kenny De Commer, Thomas Timmermann
Compact quantum groups of face type, as introduced by Hayashi, form a class of compact quantum groupoids with a classical, finite set of objects. Using the notions of a weak multip…
Quantum flag manifolds as quotients of degenerate quantized universal enveloping algebras
Kenny De Commer, Sergey Neshveyev
Let be a semi-simple Lie algebra with fixed root system, and the quantization of its universal enveloping algebra. Let be a subset…
Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure
Kenny De Commer
Let be a compact simple Lie algebra. We modify the quantized enveloping -algebra associated to by a real-valued character on the positive part of…
CCAP for universal discrete quantum groups
Kenny De Commer, Amaury Freslon, Makoto Yamashita
We show that the discrete duals of the free orthogonal quantum groups have the Haagerup property and the completely contractive approximation property. Analogous results hold for t…
Free actions of compact quantum group on unital C*-algebras
Paul F. Baum, Kenny De Commer, Piotr M. Hajac
Let F be a field, G a finite group, and Map(G,F) the Hopf algebra of all set-theoretic maps G->F. If E is a finite field extension of F and G is its Galois group, the extension is…
Tannaka-Krein duality for compact quantum homogeneous spaces. I. General theory
Kenny De Commer, Makoto Yamashita
An ergodic action of a compact quantum group G on an operator algebra A can be interpreted as a quantum homogeneous space for G. Such an action gives rise to the category of finite…
A construction of finite index C*-algebra inclusions from free actions of compact quantum groups
Kenny De Commer, Makoto Yamashita
Given an action of a compact quantum group on a unital C*-algebra, one can amplify the action with an adjoint representation of the quantum group on a finite dimensional matrix alg…
Galois objects and cocycle twisting for locally compact quantum groups
K. De Commer
In this article, we investigate the notion of a Galois object for a locally compact quantum group M. Such an object consists of a von Neumann algebra N equipped with an ergodic int…
A study of Galois objects for algebraic quantum groups
K. De Commer
We supplement the study of Galois theory for algebraic quantum groups started in the paper 'Galois Theory for Multiplier Hopf Algebras with Integrals' by A. Van Daele and Y.H. Zhan…