预投射代数与C-可排序字
Preprojective algebras and c-sortable words
摘要：
设$Q$是一个无圈环，$Λ$是$Q$在代数闭域$k$上的完全预投射代数.对于$Q$的Coxeter群中的任意元素$w$，Buan，Iyama，Reiten和Scott在\cite{Bua2}中引入并研究了一个有限维代数$Λ_w=Λ/I_w$ .在本文中，我们将研究与$w$的任何降低表达$\mathbf{w}$相关的$Λ_w$的过滤。我们对单词$\mathbf{w}$是$c$可排序的情况特别感兴趣，其中$c$是Coxeter元素。在这种情况下，该滤子的连续子可以与具有有限挠自由类的倾斜$kQ$ -模相联系。
英文摘要：
Let $Q$ be an acyclic quiver and $Λ$ be the complete preprojective algebra of $Q$ over an algebraically closed field $k$. To any element $w$ in the Coxeter group of $Q$, Buan, Iyama, Reiten and Scott have introduced and studied in \cite{Bua2} a finite dimensional algebra $Λ_w=Λ/I_w$. In this paper we look at filtrations of $Λ_w$ associated to any reduced expression $\mathbf{w}$ of $w$. We are especially interested in the case where the word $\mathbf{w}$ is $c$-sortable, where $c$ is a Coxeter element. In this situation, the consecutive quotients of this filtration can be related to tilting $kQ$-modules with finite torsionfree class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
