Homology and twisted C*-algebras for self-similar actions and Zappa-Szép products
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909276797140992 |
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| author | Mundey, Alexander Sims, Aidan |
| author_facet | Mundey, Alexander Sims, Aidan |
| contents | We study the categorical homology of Zappa-Szép products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the homology of a double complex, and so can be computed via a spectral sequence involving homology groups of the constituent categories. We give explicit formulae for the isomorphisms involved, and compute the homology of a class of examples that generalise odometers. We define the C*-algebras of self-similar groupoid actions on k-graphs twisted by 2-cocycles arising from this homology theory, and prove some fundamental results about their structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09600 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homology and twisted C*-algebras for self-similar actions and Zappa-Szép products Mundey, Alexander Sims, Aidan K-Theory and Homology Operator Algebras 18G15 (primary) 18A32, 46L05 (secondary) We study the categorical homology of Zappa-Szép products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the homology of a double complex, and so can be computed via a spectral sequence involving homology groups of the constituent categories. We give explicit formulae for the isomorphisms involved, and compute the homology of a class of examples that generalise odometers. We define the C*-algebras of self-similar groupoid actions on k-graphs twisted by 2-cocycles arising from this homology theory, and prove some fundamental results about their structure. |
| title | Homology and twisted C*-algebras for self-similar actions and Zappa-Szép products |
| topic | K-Theory and Homology Operator Algebras 18G15 (primary) 18A32, 46L05 (secondary) |
| url | https://arxiv.org/abs/2311.09600 |