报告题目：Rota-Baxter groups, post-groups and post-groupoids

主讲人：生云鹤 教授（吉林大学）

摘要：Rota-Baxter Lie algebras, post-Lie algebras and post-Lie algebroids have various important applications and it is natural to consider the corresponding global objects. We introduce the notions of Rota-Baxter groups, post-groups and post-groupoids. In particular, one can obtain  Rota-Baxter Lie algebras, post-Lie algebras and post-Lie algebroids from Rota-Baxter Lie groups, post-Lie groups and post-Lie groupoids via differentiation respectively. These global structures are related to the factorization problem, (Lie-)Butcher groups, skew-left bracs, and can be used to construct set-theoretical (quiver-theoretical) solutions of the Yang-Baxter equation. As the global objects corresponding to Rota-Baxter Lie algebras, post-Lie algebras and post-Lie algebroids,it is believed that these structures have potential  applications in many fields, e.g.  in control theory, numerical analysis, regularity structures, representation theory and differential geometry.

报告时间：2024年12月26日下午15:45 - 16:45

报告地点：（线上）腾讯会议：756-290-980

报告人简介：

生云鹤，吉林大学数学学院副院长、教授、博士生导师，吉林省政府津贴专家（省有突出贡献专家）。主要研究领域为Poisson几何、非线性李理论、高阶李理论与数学物理等。在《Adv. Math.》《Math. Ann.》《Comm. Math. Phys.》《Trans. Amer. Math. Soc.》《Int. Math. Res. Not. IMRN》《J. Noncommut. Geom.》《J. Algebra》《Pacific J. Math.》等著名期刊发表学术论文90余篇。主持国家自然科学优秀青年基金、面上项目、青年项目、天元项目以及博士后基金项目等多项课题，并担任《数学进展》、《J. Nonlinear Math. Phys.》杂志编委。