Noetherian criteria for dimer algebras
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866910283791859712 |
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| author | Beil, Charlie |
| author_facet | Beil, Charlie |
| contents | Let $A$ be a nondegenerate dimer (or ghor) algebra on a torus, and let $Z$ be its center. Using cyclic contractions, we show the following are equivalent: $A$ is noetherian; $Z$ is noetherian; $A$ is a noncommutative crepant resolution; each arrow of $A$ is contained in a perfect matching whose complement supports a simple module; and the vertex corner rings $e_iAe_i$ are pairwise isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_08047 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Noetherian criteria for dimer algebras Beil, Charlie Rings and Algebras Let $A$ be a nondegenerate dimer (or ghor) algebra on a torus, and let $Z$ be its center. Using cyclic contractions, we show the following are equivalent: $A$ is noetherian; $Z$ is noetherian; $A$ is a noncommutative crepant resolution; each arrow of $A$ is contained in a perfect matching whose complement supports a simple module; and the vertex corner rings $e_iAe_i$ are pairwise isomorphic. |
| title | Noetherian criteria for dimer algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/1805.08047 |