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.

中文翻译：

---

前投影代数和 Coxeter 群的倾斜和集群倾斜

我们研究了与箭袋的 Coxeter 群的元素 $w$ 相关的前投影代数的因子代数的稳定范畴。我们证明存在与 $w$ 的每个简化表达式 $\bf{w}$ 相关联的该类别的淤泥对象 $M(\bf{w})$ 并给出 $\bf{w}$ 的充分条件使得 $M(\bf{w})$ 是一个倾斜的物体。特别地，稳定范畴是三角形等价于$M(\bf{w})$的自同态代数的派生范畴。此外，我们将其与由 Amiot-Reiten-Todorov 给出的用于聚类类别的三角形等价进行比较。