Chain Conditions for Etale Groupoid Algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866929268830765056 |
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| author | Philip, Sunil |
| author_facet | Philip, Sunil |
| contents | Let $R$ be a unital commutative ring with unit and $\mathscr{G}$ an ample groupoid. Using the topology of the groupoid $\mathscr{G}$, Steinberg defined an etale groupoid algebra $R\mathscr{G}$. These etale groupoid algebras generalize various algebras including group algebras, commutative algebras over a field generated by idempotents, traditional groupoid algebras, Leavitt path algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg later characterized the classical chain conditions for etale groupoid algebras. We characterize categorically noetherian and artinian, locally noetherian and artinian, and semisimple etale groupoid algebras, generalizing existing results for Leavitt path algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_11816 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Chain Conditions for Etale Groupoid Algebras Philip, Sunil Rings and Algebras Operator Algebras 16P20, 16P40, 16S88, 16S99, 16D70, 16D60, 16K99, 22A22 Let $R$ be a unital commutative ring with unit and $\mathscr{G}$ an ample groupoid. Using the topology of the groupoid $\mathscr{G}$, Steinberg defined an etale groupoid algebra $R\mathscr{G}$. These etale groupoid algebras generalize various algebras including group algebras, commutative algebras over a field generated by idempotents, traditional groupoid algebras, Leavitt path algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg later characterized the classical chain conditions for etale groupoid algebras. We characterize categorically noetherian and artinian, locally noetherian and artinian, and semisimple etale groupoid algebras, generalizing existing results for Leavitt path algebras. |
| title | Chain Conditions for Etale Groupoid Algebras |
| topic | Rings and Algebras Operator Algebras 16P20, 16P40, 16S88, 16S99, 16D70, 16D60, 16K99, 22A22 |
| url | https://arxiv.org/abs/2011.11816 |