Sondre Kvamme
(NTNU)

Mathematics Seminar

Higher Auslander—Reiten theory (also called higher homological algebra) was introduced by Iyama in 2007 as a generalization of classical Auslander—Reiten theory. The main objects of study in the theory are d-cluster tilting subcategories of modules categories. It turns out that many notions in algebra and representation theory have generalization to higher Auslander—Reiten theory. In particular, in 2016 Jørgensen introduced a generalization of torsion classes, called higher torsion classes.

In this talk I will recall the definition of higher torsion classes. I will then explain how functorially finite d-torsion classes give rise to (d+1)-term silting complexes, and hence to derived equivalences. The construction is analogous to the construction of 2-term silting complexes due to Adachi-Iyama-Reiten in 2014. I will illustrate the constructions and results on higher Nakayama algebras of type A_n.

Organised by: AarHomAlg

Revised: 20.02.2024