学术报告
Tilted algebras and cycle-bounded AR-components-Prof. Dr. Shiping Liu (University of Sherbrooke, Canada)
题目：Tilted algebras and cycle-bounded AR-components
报告人：Prof. Dr. Shiping Liu (University of Sherbrooke, Canada)
时间：2017年6月15日(周四)下午2:00--3:00
地点：首都师范大学本部教学2楼613教室
摘要：In this talk, we shall talk about Auslander-Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-invertible maps between modules in the given component. First, we give a number of combinatorial characterizations of almost acyclic Auslander-Reiten components. Then, we show that an Auslander-Reiten component with bounded short cycles is closely related to connecting components of a tilted quotient algebra. As an application, we shall show that an artin algebra is of finite representation type if and only if its module category has bounded short cycles. This includes a well-known result by Ringel saying that a finite dimensional algebra is representation-finite if its module category has no cycle, and a later generalization by Happel-Liu saying that an artin algebra is of finite representation type if its module category has no short cycles.
欢迎全体师生积极参加！
