Quasi-diagrams and gentle algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911789973766144 |
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| author | Hu, Haigang Wang, Xiao-Chuang Ye, Yu |
| author_facet | Hu, Haigang Wang, Xiao-Chuang Ye, Yu |
| contents | Any gentle algebra $A$ with one maximal path corresponds to a unique quasi-diagram $α$. We introduce the regularity for $α$, and show that $A$ has finite global dimension if and only if $α$ is regular. We characterize regular quasi-diagrams which remain regular under the dihedral group action. We prove that the set of maximal chord diagrams is the "biggest" one among the sets closed under taking Koszul dual and rotations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-diagrams and gentle algebras Hu, Haigang Wang, Xiao-Chuang Ye, Yu Rings and Algebras Combinatorics 16P10, 16E10, 20B30 Any gentle algebra $A$ with one maximal path corresponds to a unique quasi-diagram $α$. We introduce the regularity for $α$, and show that $A$ has finite global dimension if and only if $α$ is regular. We characterize regular quasi-diagrams which remain regular under the dihedral group action. We prove that the set of maximal chord diagrams is the "biggest" one among the sets closed under taking Koszul dual and rotations. |
| title | Quasi-diagrams and gentle algebras |
| topic | Rings and Algebras Combinatorics 16P10, 16E10, 20B30 |
| url | https://arxiv.org/abs/2403.02986 |