Equivariant homotopy classification of graph C*-algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909295659974656 |
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| author | Bilich, Boris Dor-On, Adam Ruiz, Efren |
| author_facet | Bilich, Boris Dor-On, Adam Ruiz, Efren |
| contents | We show that shift equivalence of essential adjacency matrices coincides with gauge-equivariant homotopy equivalence of their stabilized graph C*-algebras. This provide the first equivalent formulation of shift equivalence of essential matrices in terms of gauge actions on graph C*-algebras. Our proof uses bicategory theory for C*-bimodules developed by Meyer and Sehnem, allowing us to avoid the use of K-theory classification of C*-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant homotopy classification of graph C*-algebras Bilich, Boris Dor-On, Adam Ruiz, Efren Operator Algebras Dynamical Systems Rings and Algebras Primary: 46L55, 46M15 Secondary: 37B10, 46L35, 18N10 We show that shift equivalence of essential adjacency matrices coincides with gauge-equivariant homotopy equivalence of their stabilized graph C*-algebras. This provide the first equivalent formulation of shift equivalence of essential matrices in terms of gauge actions on graph C*-algebras. Our proof uses bicategory theory for C*-bimodules developed by Meyer and Sehnem, allowing us to avoid the use of K-theory classification of C*-algebras. |
| title | Equivariant homotopy classification of graph C*-algebras |
| topic | Operator Algebras Dynamical Systems Rings and Algebras Primary: 46L55, 46M15 Secondary: 37B10, 46L35, 18N10 |
| url | https://arxiv.org/abs/2408.09740 |