Permanence of the torsion-freeness property for divisible discrete quantum subgroups

Abstract

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).

Accepted for publication in Mathematica Scandinavica

References in corpus (2)

• On bicolimits of $C^{\ast }$-categories
• Projective representation theory for compact quantum groups and the quantum Baum-Connes assembly map

Cited by in corpus (1)

• Quantum direct products and the Künneth class