学术报告（一）

报告题目：Conformal r-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and ON-structures

报告人：刘杰锋(东北师范大学)

报告时间：2022年6月30日（星期四）19:00-20:00

腾讯会议：656-599-523

参加人员：本科生、研究生、教师

报告摘要：In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an LCModP pair), which lead to the notions of Nijenhuis operator on the Lie conformal algebra and Nijenhuis structure on the LCMod pair, respectively. Then by adding compatibility conditions between Nijenhuis structures and O-operators, we introduce the notion of an ON-structure on an LCMod pair and show that an ON-structure gives rise to a hierarchy of pairwise compatible O-operators. In particular, we show that compatible O-operators on a Lie conformal algebra can be characterized by Nijenhuis operators on Lie conformal algebras. Finally, we introduce the notions of conformal r-matrix-Nijenhuis structure and symplectic-Nijenhuis structure on Lie conformal algebras and study their relations. This is a joint a work with Sihan Zhou and Lamei Yuan.

报告人简介：刘杰锋，东北师范大学数学与统计学院副教授。2016年博士毕业于吉林大学数学学院。从事Poisson几何与数学物理的研究，在J. Symplectic Geom.,J.Noncommut.Geo.,J. Algebra等杂志上发表多篇论文。

学术报告（二）

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

报告人：唐荣(吉林大学)

报告时间：2022年6月30日（星期四）20:00-21:00

腾讯会议：656-599-523

参加人员：本科生、研究生、教师

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等杂志上发表论文多篇。