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arXiv · 2212.09101

Classification silted algebras for a quiver of Dynkin type $\mathbb{A}_{n}$ via geometric models

Yu-Zhe Liu·Houjun Zhang
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Abstract

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 $A_{n}$.

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BibTeXRIS

Yu-Zhe Liu, Houjun Zhang. 2022-12-18. Classification silted algebras for a quiver of Dynkin type $\mathbb{A}_{n}$ via geometric models. https://arxiv.org/abs/2212.09101

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