Projective representations of compact quantum groups and the quantum assembly map

Abstract: The torsion phenomena play important role in the construction of the assembly map in the context of Baum-Connes conjecture. The corresponding case of quantum groups is more involved, since the torsion phenomena are not necessarily associated to torsion subgroups.An important role in this context is played by projective representations of quantum groups. We will describe the general structure of projective representations, associated twisted group C*-algebras and the related torsion phenomena for compact quantum groups.We will also describe the role that these results play in the context of the assembly map for compact quantum groups.This is ''work in progress'' joint with Kenny De Commer and Ruben Martos.

operator algebras

Audience: researchers in the topic

Conference on operator algebras and related topics in Istanbul, 2021