Representing topological full groups in Steinberg algebras and C*-algebras
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914629198807040 |
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| author | Armstrong, Becky Clark, Lisa Orloff Ghandehari, Mahya Kang, Eun Ji Yang, Dilian |
| author_facet | Armstrong, Becky Clark, Lisa Orloff Ghandehari, Mahya Kang, Eun Ji Yang, Dilian |
| contents | We study the natural representation of the topological full group of an ample Hausdorff groupoid in the groupoid's complex Steinberg algebra and in its full and reduced C*-algebras. We characterise precisely when this representation is injective and show that it is rarely surjective. We then restrict our attention to discrete groupoids, which provide unexpected insight into the behaviour of the representation of the topological full group in the full and reduced groupoid C*-algebras. We show that the image of the representation is not dense in the full groupoid C*-algebra unless the groupoid is a group, and we provide an example showing that the image of the representation may still be dense in the reduced groupoid C*-algebra even when the groupoid is not a group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_04927 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Representing topological full groups in Steinberg algebras and C*-algebras Armstrong, Becky Clark, Lisa Orloff Ghandehari, Mahya Kang, Eun Ji Yang, Dilian Operator Algebras Group Theory Rings and Algebras 16S99, 46L05 (primary), 22A22, 18B40, 20F38 (secondary) We study the natural representation of the topological full group of an ample Hausdorff groupoid in the groupoid's complex Steinberg algebra and in its full and reduced C*-algebras. We characterise precisely when this representation is injective and show that it is rarely surjective. We then restrict our attention to discrete groupoids, which provide unexpected insight into the behaviour of the representation of the topological full group in the full and reduced groupoid C*-algebras. We show that the image of the representation is not dense in the full groupoid C*-algebra unless the groupoid is a group, and we provide an example showing that the image of the representation may still be dense in the reduced groupoid C*-algebra even when the groupoid is not a group. |
| title | Representing topological full groups in Steinberg algebras and C*-algebras |
| topic | Operator Algebras Group Theory Rings and Algebras 16S99, 46L05 (primary), 22A22, 18B40, 20F38 (secondary) |
| url | https://arxiv.org/abs/2309.04927 |