题目：Tilting modules and support $\tau$-tilting modules over preprojective algebras associated with symmetrizable Cartan matrices

报告人：耿圣飞，四川大学

时间：2021年4月16日（星期五）15：00-17：00

Zoom 号：9739747578

摘要：For any given symmetrizable Cartan matrix $C$ with a symmetrizer $D$, Geiss-Leclerc-Schr\{o}er (Invent. Math. 209, 61-158 (2017)) introduced a generalized preprojective algebra $\Pi(C, D)$. We study tilting modules and support $\tau$-tilting modules for the generalized preprojective algebra $\Pi(C, D)$ and show that there is a bijection between the set of all cofinite tilting ideals of $\Pi(C,D)$ and the corresponding Weyl group $W(C)$ provided that $C$ has no component of Dynkin type. When $C$ is of Dynkin type, we also establish a bijection between the set of all basic support $\tau$-tilting $\Pi(C,D)$-modules and the corresponding Weyl group $W(C)$. These results generalize the classification results of Buan et al. (Compos. Math. 145(4), 1035–1079 (2009)) and Mizuno (Math. Zeit. 277(3), 665–690 (2014)) over classical preprojective algebras. This talk is based on joint work with Changjian Fu.