On dense subalgebras of the singular ideal in groupoid C*-algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911520636534784 |
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| author | Gonzales, Julian Hume, Jeremy B. |
| author_facet | Gonzales, Julian Hume, Jeremy B. |
| contents | We prove that ideals in amenable second-countable non-Hausdorff étale groupoid $C^*$-algebras are determined by their isotropy fibres. As an application, we characterise when the singular functions in Connes' algebra are dense in the singular ideal in terms of a property of explicit ideals in the isotropy group $C^*$-algebras. We then show this density property holds for all $C^*$-algebras of groupoids with finite-by-nilpotent isotropy groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On dense subalgebras of the singular ideal in groupoid C*-algebras Gonzales, Julian Hume, Jeremy B. Operator Algebras 22A22, 46L05 (Primary), 37A55, 22D25 (Secondary) We prove that ideals in amenable second-countable non-Hausdorff étale groupoid $C^*$-algebras are determined by their isotropy fibres. As an application, we characterise when the singular functions in Connes' algebra are dense in the singular ideal in terms of a property of explicit ideals in the isotropy group $C^*$-algebras. We then show this density property holds for all $C^*$-algebras of groupoids with finite-by-nilpotent isotropy groups. |
| title | On dense subalgebras of the singular ideal in groupoid C*-algebras |
| topic | Operator Algebras 22A22, 46L05 (Primary), 37A55, 22D25 (Secondary) |
| url | https://arxiv.org/abs/2511.04391 |