Shift equivalence relations through the lens of C*-correspondences
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916473847414784 |
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| author | Bilich, Boris Dor-On, Adam Ruiz, Efren |
| author_facet | Bilich, Boris Dor-On, Adam Ruiz, Efren |
| contents | We continue the study of shift equivalence relations from the perspective of C*-bimodule theory. We study emerging shift equivalence relations following work of the second-named author with Carlsen and Eilers, both in terms of adjacency matrices and in terms of their C*-correspondences, and orient them when possible. In particular, we show that if two regular C*-correspondences are strong shift equivalent, then the intermediary C*-correspondences realizing the equivalence may be chosen to be regular. This result provides the final missing piece in answering a question of Muhly, Pask and Tomforde, and is used to confirm a conjecture of Kakariadis and Katsoulis on shift equivalence of C*-correspondences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05598 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shift equivalence relations through the lens of C*-correspondences Bilich, Boris Dor-On, Adam Ruiz, Efren Operator Algebras Dynamical Systems Primary: 46L08, 37B10. Secondary: 37A55, 46L55 We continue the study of shift equivalence relations from the perspective of C*-bimodule theory. We study emerging shift equivalence relations following work of the second-named author with Carlsen and Eilers, both in terms of adjacency matrices and in terms of their C*-correspondences, and orient them when possible. In particular, we show that if two regular C*-correspondences are strong shift equivalent, then the intermediary C*-correspondences realizing the equivalence may be chosen to be regular. This result provides the final missing piece in answering a question of Muhly, Pask and Tomforde, and is used to confirm a conjecture of Kakariadis and Katsoulis on shift equivalence of C*-correspondences. |
| title | Shift equivalence relations through the lens of C*-correspondences |
| topic | Operator Algebras Dynamical Systems Primary: 46L08, 37B10. Secondary: 37A55, 46L55 |
| url | https://arxiv.org/abs/2411.05598 |