Speaker：Ming Lu(Sichuan University)

Time：2023-3-9, 16:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

The root category of a hereditary abelian category is a 2-periodic triangulated category, which has deep connections to Lie algebra and quantum group. In about 2006, Toen, Xiao and Xu introduced derived Hall algebras for triangulated categories satisfying some finiteness conditions, and they expressed great interest to define derived Hall algebras for root categories. This work is to solve this question. We define a derived Hall algebra of the root category by counting the triangles, which is proved to be isomorphic to the Drinfeld double of Hall algebra. When applied to the Jordan quiver or elliptic curves, these algebras provide categorical realizations of the Drinfeld double of the ring of symmetric functions and also double affine Hecke algebras. This is joint work with Jiayi Chen and Shiquan Ruan.