Quantum metrics on crossed products with groups of polynomial growth
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910720035127296 |
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| author | Austad, Are Kaad, Jens Kyed, David |
| author_facet | Austad, Are Kaad, Jens Kyed, David |
| contents | We show how to equip the crossed product between a group of polynomial growth and a compact quantum metric space with a compact quantum metric space structure. When the quantum metric on the base space arises from a spectral triple, which is compatible with the action of the group, we furthermore show that the crossed product becomes a spectral metric space. Lastly, we analyse the spectral triple at the crossed product level from the point of view of unbounded $KK$-theory and show that it arises as an internal Kasparov product of unbounded Kasparov modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12220 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum metrics on crossed products with groups of polynomial growth Austad, Are Kaad, Jens Kyed, David Operator Algebras 58B34, 47L65, 46L55 We show how to equip the crossed product between a group of polynomial growth and a compact quantum metric space with a compact quantum metric space structure. When the quantum metric on the base space arises from a spectral triple, which is compatible with the action of the group, we furthermore show that the crossed product becomes a spectral metric space. Lastly, we analyse the spectral triple at the crossed product level from the point of view of unbounded $KK$-theory and show that it arises as an internal Kasparov product of unbounded Kasparov modules. |
| title | Quantum metrics on crossed products with groups of polynomial growth |
| topic | Operator Algebras 58B34, 47L65, 46L55 |
| url | https://arxiv.org/abs/2312.12220 |