Unital shift equivalence
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909578949558272 |
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| author | Brix, Kevin Aguyar Ruiz, Efren |
| author_facet | Brix, Kevin Aguyar Ruiz, Efren |
| contents | We introduce and study a unital version of shift equivalence for finite square matrices over the nonnegative integers. In contrast to the classical case, we show that unital shift equivalence does not coincide with one-sided eventual conjugacy. We also prove that unital shift equivalent matrices define one-sided shifts of finite type that are continuously orbit equivalent. Consequently, unitally shift equivalent matrices have isomorphic topological full groups and isomorphic Leavitt path algebras, the latter being related to Hazrat's graded classification conjecture in algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unital shift equivalence Brix, Kevin Aguyar Ruiz, Efren Dynamical Systems Operator Algebras We introduce and study a unital version of shift equivalence for finite square matrices over the nonnegative integers. In contrast to the classical case, we show that unital shift equivalence does not coincide with one-sided eventual conjugacy. We also prove that unital shift equivalent matrices define one-sided shifts of finite type that are continuously orbit equivalent. Consequently, unitally shift equivalent matrices have isomorphic topological full groups and isomorphic Leavitt path algebras, the latter being related to Hazrat's graded classification conjecture in algebra. |
| title | Unital shift equivalence |
| topic | Dynamical Systems Operator Algebras |
| url | https://arxiv.org/abs/2504.09889 |