Non-traditional C*-diagonals in twisted groupoid C*-algebras
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915301370626048 |
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| author | Duwenig, Anna |
| author_facet | Duwenig, Anna |
| contents | We identify which conditions on an open normal subgroupoid of a LCH étale groupoid with twist are necessary and sufficient for the subgroupoid's reduced twisted C*-algebra to be a C*-diagonal in the ambient groupoid C*-algebra. We do so by first giving an explicit description of the Weyl groupoid and Weyl twist associated to any non-traditional Cartan subalgebra, that is, a Cartan subalgebra that is induced from a non-trivial open normal subgroupoid, as studied in [DWZ2025]. We then combine this description with Kumjian-Renault theory to establish the necessary and sufficient conditions to get a C*-diagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-traditional C*-diagonals in twisted groupoid C*-algebras Duwenig, Anna Operator Algebras 46L55, 46L05, 22A22 We identify which conditions on an open normal subgroupoid of a LCH étale groupoid with twist are necessary and sufficient for the subgroupoid's reduced twisted C*-algebra to be a C*-diagonal in the ambient groupoid C*-algebra. We do so by first giving an explicit description of the Weyl groupoid and Weyl twist associated to any non-traditional Cartan subalgebra, that is, a Cartan subalgebra that is induced from a non-trivial open normal subgroupoid, as studied in [DWZ2025]. We then combine this description with Kumjian-Renault theory to establish the necessary and sufficient conditions to get a C*-diagonal. |
| title | Non-traditional C*-diagonals in twisted groupoid C*-algebras |
| topic | Operator Algebras 46L55, 46L05, 22A22 |
| url | https://arxiv.org/abs/2505.17913 |