Preprojective algebras and \(c\)-sortable words (Q2881020)

The cluster algebras of \textit{S. Fomin} and \textit{A. Zelevinsky} [J. Am. Math. Soc. 15, 497--529 (2002; Zbl 1021.16017)] have led to categories with the \(2\)-Calabi-Yau property (\(2\)-CY for short). The authors concentrate around the more general class of stably \(2\)-CY and triangulated \(2\)-CY categories associated with elements in Coxeter groups. Let \(\Lambda\) be the complete projective algebra of an acyclic quiver \(Q\). To any element \(w\) in the Coxeter group of \(Q\), \textit{A. B. Baun, O. Iyama, I. Reiten} and \textit{J. Scott} [Compos. Math. 145, No. 4, 1035--1079 (2009; Zbl 1181.18006)] have studied a finite-dimensional algebra \(\Lambda_w=\Lambda/I_w\).NEWLINENEWLINEThe authors investigate filtrations of \(\Lambda_w\) associated to any reduced expression \textbf{w} of \(w\). Especially, in the case where the word \textbf{w} is \(c\)-sortable, where \(c\) is a Coxeter element. The consecutive quotients of this filtration are related to tilling \(kQ\)-modules with finite torsionfree class.