ICE-closed subcategories and wide tau-tilting modules


Conference Talk in International Conference on Representations of Algebras (ICRA 2020) at Online

Based on paper:


I’ll introduce ICE-closed subcategories of an abelian length category, subcategories closed under taking Images, Cokernels and Extensions. Both torsion classes and wide subcategories of an abelian category are ICE-closed. We will see that ICE-closed subcategories are precisely torsion classes in some wide subcategories. For a finite-dimensional algebra, I’ll introduce the notion of wide τ-tilting modules, and extend Adachi-Iyama-Reiten’s bijection between support τ-tilting modules and torsion classes to a bijection between wide τ-tilting modules and ICE-closed subcategories. If time permits, I’ll talk about some results on ICE-closed subcategories over hereditary algebras and Nakayama algebras. This talk is based on a joint work with Arashi Sakai (Nagoya University).

Slide (without handwriting), Slide (with handwriting), Talk Video (recording)