A dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866915025097064448 |
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| author | Herstedt, Paul |
| author_facet | Herstedt, Paul |
| contents | We prove that crossed products of fiberwise essentially minimal zero-dimensional dynamical systems have isomorphic $ K $-theory if and only if the dynamical systems are strong orbit equivalent. Under the additional assumption that the dynamical systems have no periodic points, this gives a classification theorem including isomorphism of the $ C^* $-algebras as well. We additionally explore the $ K $-theory of such crossed products and the Bratteli diagrams associated to the dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_06380 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems Herstedt, Paul Operator Algebras 46L55 (Primary) 46L35, 46L80 (Secondary) We prove that crossed products of fiberwise essentially minimal zero-dimensional dynamical systems have isomorphic $ K $-theory if and only if the dynamical systems are strong orbit equivalent. Under the additional assumption that the dynamical systems have no periodic points, this gives a classification theorem including isomorphism of the $ C^* $-algebras as well. We additionally explore the $ K $-theory of such crossed products and the Bratteli diagrams associated to the dynamical systems. |
| title | A dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems |
| topic | Operator Algebras 46L55 (Primary) 46L35, 46L80 (Secondary) |
| url | https://arxiv.org/abs/2111.06380 |