Permanence of the torsion-freeness property for divisible discrete quantum subgroups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915078924664832 |
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| author | Martos, Rubén |
| author_facet | Martos, Rubén |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12725 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Permanence of the torsion-freeness property for divisible discrete quantum subgroups Martos, Rubén Operator Algebras Category Theory Quantum Algebra Representation Theory 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). |
| title | Permanence of the torsion-freeness property for divisible discrete quantum subgroups |
| topic | Operator Algebras Category Theory Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2112.12725 |