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 Preprojective algebras and c-sortable words
 Let $Q$ be an acyclic quiver and $\Lambda$ 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 $\Lambda_w=\Lambda/I_w$. In this paper we look at filtrations of $\Lambda_w$ 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.
 Keyword(s) : preprojective algebra – quiver representation – generalized cluster category – Coxeter group – 2-Calabi-Yau triangulated category – tilting theory – cluster-tilting
 hal-00458893, version 3 http://hal.archives-ouvertes.fr/hal-00458893 oai:hal.archives-ouvertes.fr:hal-00458893 From: Claire Amiot <> Submitted on: Wednesday, 15 June 2011 10:14:38 Updated on: Wednesday, 15 June 2011 10:17:22