Quivers with relations arising from clusters of type Dn

主講人：唐孝敏 黑龍江大學(xué)教授

時(shí)間：2023年6月2日15：00

地點(diǎn)：三號(hào)樓332報(bào)告廳

舉辦單位：數(shù)理學(xué)院

主講人介紹：唐孝敏，黑龍江大學(xué)教授，博士生導(dǎo)師，數(shù)學(xué)學(xué)院院長，黑龍江省數(shù)學(xué)會(huì)副理事長，黑龍江大學(xué)大型科學(xué)計(jì)算實(shí)驗(yàn)室主任。主要研究李理論及相關(guān)方向，參加和主持國家自然科學(xué)基金、黑龍江省自然科學(xué)基金、黑龍江省教育廳項(xiàng)目等各類科研項(xiàng)目10余項(xiàng)，發(fā)表被SCI收錄的學(xué)術(shù)論文40余篇。

內(nèi)容介紹：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.