Topological full groups, invertible isometries, and automorphisms of groupoid algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908662626254848 |
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| author | Gardella, Eusebio Palmstrøm, Mathias Thiel, Hannes |
| author_facet | Gardella, Eusebio Palmstrøm, Mathias Thiel, Hannes |
| contents | We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the groupoid $\mathcal{G}$ is also effective, then we show that the group of (inner) automorphisms in pseudofunction algebras is a split extension of the automorphisms (respectively, the topological full group) of $\mathcal{G}$ by the group of 1-cocycles (respectively, the 1-coboundaries). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological full groups, invertible isometries, and automorphisms of groupoid algebras Gardella, Eusebio Palmstrøm, Mathias Thiel, Hannes Operator Algebras Functional Analysis We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the groupoid $\mathcal{G}$ is also effective, then we show that the group of (inner) automorphisms in pseudofunction algebras is a split extension of the automorphisms (respectively, the topological full group) of $\mathcal{G}$ by the group of 1-cocycles (respectively, the 1-coboundaries). |
| title | Topological full groups, invertible isometries, and automorphisms of groupoid algebras |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2511.14541 |