Tilting and cluster tilting for preprojective algebras and Coxeter groups
Tilting and cluster tilting for preprojective algebras and Coxeter groups
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DOI：
10.1093/imrn/rnx265
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发表时间：
2016-07
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影响因子：
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通讯作者：
Y. Kimura
中科院分区：
文献类型：
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作者：
Y. Kimura
我们研究了箭图的Coxeter群的一个元素$w$所对应的准投射代数的因子代数的稳定范畴。证明了该范畴存在一个淤积对象$M(\bf{w})$，它与$w$的每个约化表达式$\bf{w}$有关，并给出了$M(\bf{w})$是倾斜对象的一个充分条件.特别地，稳定范畴是与$M(\bf{w})$的自同态代数的派生范畴等价的三角形范畴。此外，我们将其与Amiot-Reiten-Todorov关于簇范畴的三角形等价进行了比较。
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.