Classification silted algebras for a quiver of Dynkin type $\mathbb{A}_{n}$ via geometric models
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916382005788672 |
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| author | Liu, Yu-Zhe Zhang, Houjun |
| author_facet | Liu, Yu-Zhe Zhang, Houjun |
| contents | Let $\Q$ be the quiver of Dynkin type $\mathbb{A}_n$ with linear orientation and $A_{n}=k\Q$. In this paper, we give a complete classification of the silted algebras of type $A_{n}$ by using the geometric models of gentle algebras. We show that any finite-dimensional algebra is a silted of type $A_{n}$ if and only if it is a tilted of type $A_{n}$ or a tilted algebra of type $A_{m}\times A_{n-m}$ for any positive integer $1\leq m\leq n-1$. Based on the classification, we obtain a formula for computing the number of silted algebras of type $A_{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_09101 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Classification silted algebras for a quiver of Dynkin type $\mathbb{A}_{n}$ via geometric models Liu, Yu-Zhe Zhang, Houjun Representation Theory 05E10, 16G10, 16E45 Let $\Q$ be the quiver of Dynkin type $\mathbb{A}_n$ with linear orientation and $A_{n}=k\Q$. In this paper, we give a complete classification of the silted algebras of type $A_{n}$ by using the geometric models of gentle algebras. We show that any finite-dimensional algebra is a silted of type $A_{n}$ if and only if it is a tilted of type $A_{n}$ or a tilted algebra of type $A_{m}\times A_{n-m}$ for any positive integer $1\leq m\leq n-1$. Based on the classification, we obtain a formula for computing the number of silted algebras of type $A_{n}$. |
| title | Classification silted algebras for a quiver of Dynkin type $\mathbb{A}_{n}$ via geometric models |
| topic | Representation Theory 05E10, 16G10, 16E45 |
| url | https://arxiv.org/abs/2212.09101 |