The triangulated Auslander-Iyama correspondence, I

Abstract: In these two talks, we will start by introducing a result which establishes the existence and uniqueness of (DG) enhancements for triangulated categories which admit an additive generator whose endomorphism algebra is finite-dimensional (over a perfect field). We will then present a generalisation of this result that allows us to treat a larger class of triangulated categories, which instead admit a generator with a strong regularity property (a so-called dZ-cluster tilting object). We will also explain how our result, combined with crucial theorems of August and Hua-Keller, leads to a positive solution of the Donovan-Wemyss Conjecture for contraction algebras as observed by Keller. We will also comment on some details about the proof.

K-theory and homologyquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Paris algebra seminar

Series comments: For the Zoom links and passwords, please subscribe to the mailing list (link and password will be emailed shortly before each talk) or contact one of the organizers. The slides and notes are available here. For recordings of talks, please contact Bernhard Keller.