ICE-closed subcategories over module categories


Seminar Talk in Kyoto Representation Theory Seminar at Online

Based on paper:


In the representation theory of algebras, the study of subcategories of module categories has been one of the main topics, and is related to many areas. Among them, torsion classes and wide subcategories are important and have been studied by many people. In this talk, I will introduce the notion of ICE-closed subcategories of module categories, which are closed under taking Images, Cokernels and Extensions. This class contains both torsion classes and wide subcategories. In the representation category of a Dynkin quiver, they bijectively correspond to rigid representations. For a general finite-dimensional algebra, I will explain how to classify ICE-closed subcategories using the poset structure of torsion classes, or using τ-tilting theory. This talk is based on my joint work with Arashi Sakai (Nagoya).

Talk note (4.4 MB), Talk Video (Rehearsal)