On the torsion-freeness property for divisible discrete quantum subgroups

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On the torsion-freeness property for divisible discrete quantum subgroups. / Martos Prieto, Ruben.

arxiv.org, 2021.

Research output: Working paper › Preprint › Research

Harvard

Martos Prieto, R 2021 'On the torsion-freeness property for divisible discrete quantum subgroups' arxiv.org. <https://arxiv.org/abs/2112.12725>

APA

Martos Prieto, R. (2021). On the torsion-freeness property for divisible discrete quantum subgroups. arxiv.org. https://arxiv.org/abs/2112.12725

Vancouver

Martos Prieto R. On the torsion-freeness property for divisible discrete quantum subgroups. arxiv.org. 2021.

Author

Martos Prieto, Ruben. / On the torsion-freeness property for divisible discrete quantum subgroups. arxiv.org, 2021.

Bibtex

@techreport{127df826229e4fde99d6102ebca0593b,
title = "On 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). Finally, we analyze an alternative approach to tackle the stability of torsion-freeness by divisible discrete quantum subgroups in terms of module C*-categories.",
keywords = "Faculty of Science, Baum-Connes conjecture, compact/discrete quantum groups, C*-tensor categories, divisible discrete quantum subgroups, module C*-categories, torsion, triangulated categories",
author = "{Martos Prieto}, Ruben",
year = "2021",
language = "English",
publisher = "arxiv.org",
type = "WorkingPaper",
institution = "arxiv.org",

}

RIS

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