Tilting and cluster tilting for preprojective algebras and Coxeter groups

Abstract

We study the stable category of the factor algebra of the preprojective algebra associated with an element $w$ of the Coxeter group of a quiver. We show that there exists a silting object $M(\mathbf{w})$ of this category associated with each reduced expression $\mathbf{w}$ of $w$ and give a sufficient condition on $\mathbf{w}$ such that $M(\mathbf{w})$ is a tilting object. In particular, the stable category is triangle equivalent to the derived category of the endomorphism algebra of $M(\mathbf{w})$. Moreover, we compare it with a triangle equivalence given by Amiot-Reiten-Todorov for a cluster category.

22 pages, minor changes

Cited by in corpus (2)

• Homological dimension formulas for trivial extension algebras
• Singularity categories of derived categories of hereditary algebras are derived categories