Quivers with relations arising from clusters of type Dn


主讲人:唐孝敏 黑龙江大学教授





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.