Aaron Chan (Nagoya), Generalising (pre)cluster-tilting theory.

Abstract:

The major class of examples of (d-)cluster-tilting modules can be obtained by iteratively applying (d-)AR translations on a (d-)representation-finite (d-)hereditary algebra. What if we replace "d" here by a mixture of integers? From the perspective of detecting (d-)representation-finiteness, we arrive in a class of algebras - what we call Serre-formal algebras - that generalises (d-)hereditary algebras. We will explain why, when one wants to generalise (higher) Auslander correspondence, the Serre-formal algebras do not seem to be the correct thing to look at, and also explain what is the correct thing in this framework, if time permits. This contains joint works with Osamu Iyama and Rene Marczinzik.