报告题目：An Introduction to Auslander-Reiten Theory
报告人： Raziyeh Diyanatnezhad 博士
主持人： 张毅 副教授
报告时间：北京时间10月15日，周三上午10:00-11:00,周三下午16：00-17：00
报告地点：藕舫楼725室
报告摘要：Representation theory is a powerful framework for studying abstract algebraic structures by representing their elements as linear transformations on vector spaces. In this talk, we will explore the representation theory of finite-dimensional algebras over a field. A fundamental goal is to understand the category of finitely generated modules, which can be surprisingly complex even for algebras defined by simple quivers. We will begin by introducing the essential concepts: quivers, path algebras, and their representations. We will see how to approach the classification of indecomposable modules, which are the fundamental building blocks of the module category. The core of the talk will be an introduction to the profound work of Maurice Auslander and Idun Reiten. Auslander-Reiten theory provides a homological framework to systematically uncover the hidden structure of module categories. We will define and explore its central tools: Irreducible Morphisms: The morphisms that cannot be factored non-trivially, serving as the "atomic" maps between modules. We will illustrate these concepts with key examples, such as algebras of finite representation type. In the final part of the talk, we will journey beyond the classical setting into Higher Auslander-Reiten Theory. This modern development, pioneered by Osamu Iyama, generalizes the classical theory from the framework of abelian categories to higher-dimensional homological algebra.
报告人简介：Raziyeh now is a researcher at the university of Isfahan and a Non-Resident researcher at the Institute for Research in Fundamental Sciences (IPM). She completed her PhD in Pure Mathematics at the University of Isfahan in 2023. Her research focuses on the representation theory of algebras, with a specific interest in Higher Auslander-Reiten theory and n-hereditary algebras.
欢迎广大师生踊跃参加！
数学与统计学院
江苏省系统建模与数据分析国际合作联合实验室
江苏省应用数学（南京信息工程大学）中心
2025年10月15日
