Quivers with relations arising from clusters of type Dn

主讲人：唐孝敏 黑龙江大学教授

时间：2023年6月2日15：00

地点：三号楼332报告厅

举办单位：数理学院

主讲人介绍：唐孝敏，黑龙江大学教授，博士生导师，数学学院院长，黑龙江省数学会副理事长，黑龙江大学大型科学计算实验室主任。主要研究李理论及相关方向，参加和主持国家自然科学基金、黑龙江省自然科学基金、黑龙江省教育厅项目等各类科研项目10余项，发表被SCI收录的学术论文40余篇。

内容介绍：Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. Let U be a cluster algebra of type Dn. For each cluster C of U, we define combinatorially an oriented quiver Q(C) . We also associate to C an abelian category F(C) such that the indecomposable objects of F(C) are in natural correspondence with the cluster variables of U which are not in C. We show that the denominators of the cluster variables as Laurent polynomial in C are described by indecomposables of the category F(C) of representations of Q(C) with some relations R(C) . We give an algebraic realization and a geometric realization of F(C). This generalized the results of cluster algebra of simply-laced type from An to Dn.