Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911697717952512 |
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| author | Meyer, Ralf |
| author_facet | Meyer, Ralf |
| contents | A groupoid correspondence on an etale, locally compact groupoid induces a C*-correspondence on its groupoid C*-algebra. We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant subset of the groupoid is again a groupoid C*-algebra for a certain groupoid. We describe this groupoid explicitly and characterise it by a universal property that specifies its actions on topological spaces. Our construction unifies the construction of groupoids underlying the C*-algebras of topological graphs and self-similar groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences Meyer, Ralf Operator Algebras 46L55 A groupoid correspondence on an etale, locally compact groupoid induces a C*-correspondence on its groupoid C*-algebra. We show that the Cuntz-Pimsner algebra for this C*-correspondence relative to an ideal associated to an open invariant subset of the groupoid is again a groupoid C*-algebra for a certain groupoid. We describe this groupoid explicitly and characterise it by a universal property that specifies its actions on topological spaces. Our construction unifies the construction of groupoids underlying the C*-algebras of topological graphs and self-similar groups. |
| title | Groupoid models for relative Cuntz-Pimsner algebras of groupoid correspondences |
| topic | Operator Algebras 46L55 |
| url | https://arxiv.org/abs/2506.19569 |