arXiv subjects

Kenny De Commer

Publications and source records attributed to Kenny De Commer.

39 records · Page 3Linked to original sources

arXiv2010

Comonoidal W*-Morita equivalence for von Neumann bialgebras

A theory of Galois co-objects for von Neumann bialgebras is introduced. This concept is closely related to the notion of comonoidal W*-Morita equivalence between von Neumann bialgebras, which is a Morita equivalence taking the comultiplication structure into account. We show that the property of `being a von Neumann algebraic quantum group' (i.e. `having invariant weights') is preserved under this equivalence relation. We also introduce the notion of a projective corepresentation for a von Neumann bialgebra, and show how it leads to a construction method for Galois co-objects and comonoidal W*-Morita equivalences.

math.OA↗

arXiv2009

A note on the von Neumann algebra underlying some universal compact quantum groups

We show that for F an invertible 2 by 2 matrix, the von Neumann algebra associated to the universal quantum group A_u(F) is a free Araki-Woods factor.

math.OA↗

arXiv2009

On cocycle twisting of compact quantum groups

In this article, we give a class of examples of compact quantum groups and unitary 2-cocycles on them, such that the twisted quantum groups are non-compact, but still locally compact quantum groups (in the sense of Kustermans and Vaes). This also provides examples of cocycle twists where the underlying C*-algebra of the quantum group changes.

math.OA↗