CCNU 代数学系列报告 (六)：Post-Hopf algebras and relative Rota-Baxter operators

发布时间：2022-11-14 作者：浏览次数：

Speaker:	黎允楠	DateTime:	2022年11月18日（周五）10:30-11:30
Brief Introduction to Speaker: 黎允楠，广州大学数学与信息科学学院副教授，研究方向为李代数、量子群与代数组合，已在国际知名数学期刊 Math.Z.,J. Combin. Theory Ser. A, JA, J. Algebraic Combin.等发表论文10余篇。		Place:	腾讯会议 : 31815304736
Abstract:First we introduce the notion of a post-Hopf algebra,which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra.A novel property is that a cocommutative post-Hopf algebra gives rise to a generalized Grossman-Larsson product,which leads to a subadjacent Hopf algebra.As our main examples, we discuss the post-Hopf algebra structures recovering the Grossman-Larson Hopf algebra of ordered rooted trees and the Connes-Kreimer Hopf algebra of rooted trees.Next we introduce the notion of relative Rota-Baxter operators on Hopf algebras, generalizing Goncharov’s Rota-Baxter Hopf algebras.A cocommutative post-Hopf algebra gives rise to a relative Rota-Baxter operator on its subadjacent Hopf algebra.Conversely, a relative Rota-Baxter operator also induces a post-Hopf algebra.This is joint work with Yunhe Sheng and Rong Tang.