On support $τ$-tilting graphs of gentle algebras
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909105400053760 |
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| author | Fu, Changjian Geng, Shengfei Liu, Pin Zhou, Yu |
| author_facet | Fu, Changjian Geng, Shengfei Liu, Pin Zhou, Yu |
| contents | Let $A$ be a finite-dimensional gentle algebra over an algebraically closed field. We investigate the combinatorial properties of support $τ$-tilting graph of $A$. In particular, it is proved that the support $τ$-tilting graph of $A$ is connected and has the so-called reachable-in-face property. This property was conjectured by Fomin and Zelevinsky for exchange graphs of cluster algebras which was recently confirmed by Cao and Li. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_01925 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On support $τ$-tilting graphs of gentle algebras Fu, Changjian Geng, Shengfei Liu, Pin Zhou, Yu Representation Theory Combinatorics Rings and Algebras Let $A$ be a finite-dimensional gentle algebra over an algebraically closed field. We investigate the combinatorial properties of support $τ$-tilting graph of $A$. In particular, it is proved that the support $τ$-tilting graph of $A$ is connected and has the so-called reachable-in-face property. This property was conjectured by Fomin and Zelevinsky for exchange graphs of cluster algebras which was recently confirmed by Cao and Li. |
| title | On support $τ$-tilting graphs of gentle algebras |
| topic | Representation Theory Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2108.01925 |