Preprojective algebras, skew group algebras and Morita equivalences

报告专家: 汪任(合肥工业大学)



报告摘要:Let $\mathbb{K}$ be a field of characteristic $p$ and $G$ be a cyclic $p$-group which acts on a finite acyclic quiver $Q$. The folding process associates a Cartan triple to the action. We establish a Morita equivalence between the skew group algebra of the preprojective algebra of $Q$  and the generalized preprojective algebra associated to the Cartan triple in the sense of Geiss, Leclerc and Schr\"{o}er. The Morita equivalence induces an isomorphism between certain ideal monoids of these preprojective algebras, which is compatible with the embedding of Weyl groups appearing in the folding process. This is a joint work with Xiao-Wu Chen.


专家简介:汪任,合肥工业大学副教授,2017年博士毕业于中国科学技术大学, 2018-2019期间德国斯图加特大学访问学者。 研究方向是代数表示论。目前已在J. Algebra, J. Pure Appl. Algebra等高水平SCI杂志上发表论文数篇。