题目: Cluster-concealed algebras
报告人: Claus Michael Ringel
时间: 2010年11月25日下午1:30--2:30
地点: 数学楼102室
摘要: The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects T in cluster categories. We call such an algebra cluster-concealed in case T is obtained from a preprojective tilting module. For example, all representation-finite cluster-tilted algebras are cluster-concealed. If C is a representation-finite cluster-tilted algebra, then the indecomposable C-modules are shown to be determined by their dimension vectors. For a general cluster-tilted algebra C, we are going to describe the dimension vectors of the indecomposable C-modules in terms of a Kac-Moody root system. But note that here the roots may have both positive and negative coordinates and we have to take absolute values.