Standard Auslander-Reiten components and cluster structure of infinite Dynkin type

报告题目Standard Auslander-Reiten components and cluster structure of  infinite Dynkin type


报告人Professor Shiping Liu(刘石平教授)Université de Sherbrooke






摘要Standard Auslander-Reiten components play an important role in the representation theory of finite dimensional algebras, since the maps between modules in such a component are completely described in a pure combinatorial way.  A general description of standard components of a module category has been given by Skowronski.The purpose of this talk is to extend this study to the Krull-Schmidt setting. We first give criterions for an Auslander-Reiten component of a Krull-Schmidt category with a section to be standard. Applying these results to representation categories of quivers and their bounded derived categories, we get many new types of standard components. In particular, this enables us to show that the cluster category of an infinite Dynkin type admits an infinite cluster structure formed by the tilting subcategories.




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