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arXiv · 1002.4131

Preprojective algebras and c-sortable words

Claire Amiot·Osamu Iyama·Idun Reiten·Gordana Todorov
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Abstract

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.

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Claire Amiot, Osamu Iyama, Idun Reiten, Gordana Todorov. 2011-06-15. Preprojective algebras and c-sortable words. https://doi.org/10.1112/plms%2Fpdr020

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