Higher Auslander-Reiten Theory via Bounded Derived Categories

Emre Sen (Iowa City, IA)

October 4, 2024 

Abstract: In this talk, we explore how certain full subcategories of the bounded derived category of a small abelian category yield new constructions and results in higher homological algebra, with a focus on higher Auslander algebras and higher preprojective algebras in relation to the fundamental domains of cluster categories. The main tool utilized is the endomorphism algebra construction. Additionally, we present the first example of a d-abelian category with infinitely many objects, addressing an open question since the introduction of d-cluster tilting subcategories by O. Iyama. These results are part of joint works with O. Iyama, G. Todorov and with P. Jørgensen.