Home Article

Introduction to Categorification of quasi cluster morphisms

2020-12-27

Speaker: Prof. Bernhard Keller, University of Paris

Venue: Room 314, Ouyang Building, Yuquan Campus

Abstract:

Quasi cluster morphisms were introduced by Chris Fraser (Adv. in Appl. Math. 2016) in his thesis under the supervision of Sergey Fomin. They are certain algebra morphisms between cluster algebras all of whose coefficients are invertible. We propose a categorical lift of this notion. For simplicity, we will first suppose that the given cluster algebra with non invertible coefficients admits a Frobenius categorification. We will show how the passage from the Frobenius category to its derived category lifts the localization at the coefficients and how this framework leads to a simple categorical lift of the notion of quasi cluster morphism. We will then sketch the extension to arbitrary (skewsymmetric) cluster algebras with geometric coefficients based on relative Ginzburg algebras. This last part is based on work by Yilin Wu in his ongoing Ph. D. thesis.