陈建功大讲堂——代数讲坛（2022-11）

报告题目：(Lie-)Butcher groups, post-groups and the Yang-Baxter equation

报告人：唐荣

报告时间：9月22日 10：00-11：00

报告地点：腾讯会议：446 544 147

报告摘要：In this talk, first we introduce the notion of a post-group, which is an integral object of a post-Lie algebra. Then we find post-group structures on Butcher group and $\huaP$-group of an operad $\huaP$. Next we show that a relative Rota-Baxter operator on a group naturally split the group structure to a post-group structure. Conversely, a post-group gives rise to a relative Rota-Baxter operator on the subadjacent group. We prove that a post-group gives a braided group and a solution of the Yang-Baxter equation. Moreover, we obtain that the category of post-groups is isomorphic to the category of braided groups and the category of skew-left braces. What's more, we give the definition of a post-Lie group and show that there is a post-Lie algebra structure on the vector space of left invariant vector fields, which verifies that post-Lie groups are the integral objects of post-Lie algebras. Finally, we utilize the post-Hopf algebras and post-Lie Magnus expansion to study the formal integration of post-Lie algebras.

报告人简介：唐荣，吉林大学讲师。从事Rota-Baxter代数和Yang-Baxter方程的研究。在Communications in Mathematical Physics，Journal of the Institute of Mathematics of Jussieu, Journal of Noncommutative Geometry，Journal of Algebra等SCI杂志上发表论文近20篇。