On the torsion-freeness property for divisible discrete quantum subgroups

Research output: Working paperPreprintResearch

We prove that torsion-freeness in the sense of Meyer-Nest is preserved under divisible discrete quantum subgroups. As a consequence, we obtain some stability results of the torsion-freeness property for relevant constructions of quantum groups (quantum (semi-)direct products, compact bicrossed products and quantum free products). We improve some stability results concerning the Baum-Connes conjecture appearing already in a previous work of the author. For instance, we show that the (resp. strong) Baum-Connes conjecture is preserved by discrete quantum subgroups (without any torsion-freeness or divisibility assumption). Finally, we analyze an alternative approach to tackle the stability of torsion-freeness by divisible discrete quantum subgroups in terms of module C*-categories.
Original languageEnglish
Publisherarxiv.org
Number of pages32
Publication statusPublished - 2021

    Research areas

  • Faculty of Science - Baum-Connes conjecture, compact/discrete quantum groups, C*-tensor categories, divisible discrete quantum subgroups, module C*-categories, torsion, triangulated categories

Links

ID: 312338653