Derived Hall algebras of root categories

：卢明（四川大学）
：2023-03-09 16:00
：厦大海韵园数理大楼天元会议室686

报告人：卢明（四川大学）

时  间：2023年3月9日下午16:00-17:30

地  点：厦大海韵园数理大楼天元会议室686

内容摘要:

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.

个人简介：

卢明，四川大学副教授，入选2022年度“万人计划”青年拔尖人才，研究兴趣为代数表示论与李理论。目前主要从事量子群和i-量子群的Hall代数实现和几何实现的研究，在Proc. London Math. Soc, Adv. Math, Comm. Math.Phys.等数学杂志上发表20余篇论文。

 

联系人：阮诗佺