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 $M(\bf{ w})$ of this category associated with each reduced expression $\bf{ w}$ of $w$ and give a sufficient condition on $\bf{ w}$ such that $M(\bf{ w})$ is a tilting object. In particular, the stable category is triangle equivalent to the derived category of the endomorphism algebra of $M(\bf{ w})$. Moreover, we compare it with a triangle equivalence given by Amiot-Reiten-Todorov for a cluster category.
Categories: math.RT