Relative Cluster categories and Higgs categories
Organizers
Speaker
Yilin Wu
Time
Wednesday, December 4, 2024 2:00 PM - 3:00 PM
Venue
Shuangqing-C548
Online
Zoom 388 528 9728
(BIMSA)
Abstract
Cluster categories were introduced in 2006 by Buan-Marsh-Reineke-Reiten-Todorov in order to categorify acyclic cluster algebras without coefficients. Their construction was generalized by Amiot and Plamondon to arbitrary cluster algebras associated with quivers (2009 and 2011). A higher dimensional generalization is due to Guo (2011). Cluster algebras with coefficients are important since they appear in nature as coordinate algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells,.... The work of Geiss-Leclerc-Schröer often yields Frobenius exact categories which allow to categorify such cluster algebras. In this talk, we will present the construction of the Higgs category (generalizing GLS'Frobenius categories E) and of the relative cluster category (generalizing the derived category of E) by using Ginzburg morphism which carries a canonical relative left 3-Calabi-Yau structure.