[집중강연 2021.02.01~05] Auslander-Reiten translation and $\tau$-tilting theory

Schedule

Feb 1 (Mon) ~ 5 (Fri), 14:00 ~ 15:30 in Seoul time every day

 

 

Place

Zoom online

 

 

Speaker

Sota Asai (Osaka University)

 

 

Title
Auslander-Reiten translation and $\tau$-tilting theory

 

Abstract
In the representation theory of finite dimensional algebras, Auslander-Reiten (AR) translation is an important tool to understand the modules. In these lectures, I first recall some basic properties of algebras including quiver representations. Then, I will explain some properties and explicit calculations of AR translation. After that, I would like to show you how AR translation is related to classical tilting theory and $\tau$-tilting theory.

 

 

Contents

Topic 1 (Feb 1): Finite-dimensional algebras and modules ([ASS] Chapter 1) 

 

Topic 2 (Feb 2): Bound quivers and their representations ([ASS] Chapter 2-3)

 

Topic 3 (Feb 3): Auslander--Reiten theory ([ASS] Chapter 4)

 

Topic 4 (Feb 4): Classical tilting theory ([ASS] Chapter 6)

 

Topic 5 (Feb 5): $\tau$-tilting theory ([AIR])

 

*each topic a 90min lecture

*Lecture notes

 

 

References

1. [Ass] Assem, Skowronski, Simson, Elements of the Representation Theory of Associative Algebras, 2006(http://doi.org/10.1017/CBO9780511614309)

2. [AIR] Adachi, Iyama, Reiten, $\tau$-tilting theory, 2014 (https://doi.org/10.1112/S0010437X13007422)