Splittings for C*-correspondences and strong shift equivalence
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910769859264512 |
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| author | Brix, Kevin Aguyar Mundey, Alexander Rennie, Adam |
| author_facet | Brix, Kevin Aguyar Mundey, Alexander Rennie, Adam |
| contents | We present an extension of the notion of in-splits from symbolic dynamics to topological graphs and, more generally, to C*-correspondences. We demonstrate that in-splits provide examples of strong shift equivalences of C*-correspondences. Furthermore, we provide a streamlined treatment of Muhly, Pask, and Tomforde's proof that any strong shift equivalence of regular C*-correspondences induces a (gauge-equivariant) Morita equivalence between Cuntz-Pimsner algebras. For topological graphs, we prove that in-splits induce diagonal-preserving gauge-equivariant *-isomorphisms in analogy with the results for Cuntz-Krieger algebras. Additionally, we examine the notion of out-splits for C*-correspondences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01917 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Splittings for C*-correspondences and strong shift equivalence Brix, Kevin Aguyar Mundey, Alexander Rennie, Adam Operator Algebras Dynamical Systems 46L55 (Primary), 37A55, 46L08 (Secondary) We present an extension of the notion of in-splits from symbolic dynamics to topological graphs and, more generally, to C*-correspondences. We demonstrate that in-splits provide examples of strong shift equivalences of C*-correspondences. Furthermore, we provide a streamlined treatment of Muhly, Pask, and Tomforde's proof that any strong shift equivalence of regular C*-correspondences induces a (gauge-equivariant) Morita equivalence between Cuntz-Pimsner algebras. For topological graphs, we prove that in-splits induce diagonal-preserving gauge-equivariant *-isomorphisms in analogy with the results for Cuntz-Krieger algebras. Additionally, we examine the notion of out-splits for C*-correspondences. |
| title | Splittings for C*-correspondences and strong shift equivalence |
| topic | Operator Algebras Dynamical Systems 46L55 (Primary), 37A55, 46L08 (Secondary) |
| url | https://arxiv.org/abs/2305.01917 |