On the socle of a class of Steinberg algebras
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913701975556096 |
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| author | Clark, Lisa Orloff Canto, Cristóbal Gil Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz |
| author_facet | Clark, Lisa Orloff Canto, Cristóbal Gil Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz |
| contents | We study minimal left ideals in Steinberg algebras of Hausdorff groupoids. We establish a relationship between minimal left ideals in the algebra and open singletons in the unit space of the groupoid. We apply this to obtain results about the socle of Steinberg algebras under certain hypotheses. This encompasses known results about Leavitt path algebras and improves on Kumjian-Pask algebra results to include higher-rank graphs that are not row-finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the socle of a class of Steinberg algebras Clark, Lisa Orloff Canto, Cristóbal Gil Barquero, Dolores Martín González, Cándido Martín Campos, Iván Ruiz Operator Algebras Rings and Algebras 16S99, 22A22, 16D25, 16D70, 18B40, 46L55, 16S88 We study minimal left ideals in Steinberg algebras of Hausdorff groupoids. We establish a relationship between minimal left ideals in the algebra and open singletons in the unit space of the groupoid. We apply this to obtain results about the socle of Steinberg algebras under certain hypotheses. This encompasses known results about Leavitt path algebras and improves on Kumjian-Pask algebra results to include higher-rank graphs that are not row-finite. |
| title | On the socle of a class of Steinberg algebras |
| topic | Operator Algebras Rings and Algebras 16S99, 22A22, 16D25, 16D70, 18B40, 46L55, 16S88 |
| url | https://arxiv.org/abs/2502.15574 |