On the torsion-freeness property for divisible discrete quantum subgroups
Publikation: Working paper › Preprint › Forskning
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On the torsion-freeness property for divisible discrete quantum subgroups. / Martos Prieto, Ruben.
arxiv.org, 2021.Publikation: Working paper › Preprint › Forskning
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TY - UNPB
T1 - On the torsion-freeness property for divisible discrete quantum subgroups
AU - Martos Prieto, Ruben
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Faculty of Science
KW - Baum-Connes conjecture
KW - compact/discrete quantum groups
KW - C-tensor categories
KW - divisible discrete quantum subgroups
KW - module C-categories
KW - torsion
KW - triangulated categories
M3 - Preprint
BT - On the torsion-freeness property for divisible discrete quantum subgroups
PB - arxiv.org
ER -
ID: 312338653