论文标题
通过几何模型的Dynkin类型$ \ mathbb {a} _ {a} _ {a} _的分类淤积代数
Classification silted algebras for a quiver of Dynkin type $\mathbb{A}_{n}$ via geometric models
论文作者
论文摘要
令$ \ q $为dynkin型$ \ mathbb {a} _n $的Quiver，带有线性定向，$ a_ {n} = k \ q $。在本文中，我们通过使用柔和代数的几何模型对$ a_ {n} $的淤泥代数进行完整分类。我们表明，任何有限维代数都是$ a_ {n} $ type typer的淤积，仅当它是$ a_ {n} $ type type typle的倾斜度或类型$ a_ {m} \ times a_ {m} \ times a_ {m} \ times a_ {n-m} $的倾斜代数。基于分类，我们获得了计算$ a_ {n} $的淤泥代数数量的公式。
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 $A_{n}$.
