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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2106.06985 |
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| _version_ | 1866909105388519424 |
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| author | Fu, Changjian Geng, Shengfei |
| author_facet | Fu, Changjian Geng, Shengfei |
| contents | We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let $Q$ be the Gabreil quiver of the endomorphism algebra of a basic cluster-tilting object in the cluster category $\mathcal{C}_\mathbb{X}$ of a weighted projective line $\mathbb{X}$. It is proved that there exists a quiver $Q'$ in the mutation equivalence class $\operatorname{Mut}(Q)$ such that $Q'$ admits a maximal green sequence. On the other hand, there is a quiver in $\operatorname{Mut}(Q)$ which does not admit a maximal green sequence if and only if $\mathbb{X}$ is of wild type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_06985 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On maximal green sequence for quivers arising from weighted projective lines Fu, Changjian Geng, Shengfei Representation Theory Combinatorics We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let $Q$ be the Gabreil quiver of the endomorphism algebra of a basic cluster-tilting object in the cluster category $\mathcal{C}_\mathbb{X}$ of a weighted projective line $\mathbb{X}$. It is proved that there exists a quiver $Q'$ in the mutation equivalence class $\operatorname{Mut}(Q)$ such that $Q'$ admits a maximal green sequence. On the other hand, there is a quiver in $\operatorname{Mut}(Q)$ which does not admit a maximal green sequence if and only if $\mathbb{X}$ is of wild type. |
| title | On maximal green sequence for quivers arising from weighted projective lines |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2106.06985 |