Preprojective algebras and c-sortable words

Details Preprojective algebras and c-sortable words Preprojective algebras and c-sortable words

2010-02-22

arxiv.org/abs/1002.4131v3

Mathematics

Representation Theory

There was a mistake in section 4 of the previous version. This section is removed in this new version. Some results still true

Scientific paper

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.

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