Higher Auslander Algebras, Cluster Tilting Objects and Preprojective Algebras Coming from Dynkin Diagrams

Gordana Todorov (Boston, MA)

November 8, 2024 

Abstract: A well-known theorem of Maurice Auslander about artin algebras describes the correspondence between {algebras A of finite representation type} and {algebras B, with gl.dim.B ≤ 2 ≤ dom.dim.B}, The correspondence is given by B := EndA(M) where M is an additive generator of modA. (now called Auslander algebras).

Higher Auslander algebras were introduced by Osamu Iyama. This talk will be about families of higher Auslander algebras and related notions of higher Cluster Tilting Objects and also higher Preprojective algebras, all constructed from the fundamental domains of cluster categories of Dynkin quivers as introduced in the original works of Emre Sen. (Joint work with Osamu Iyama and Emre Sen)