On the integration of Rota-Baxter Lie algebra and post-Lie algebra

：生云鹤（吉林大学）
：2024-05-24 08:00
：海韵园实验楼105报告厅

报告人：生云鹤（吉林大学）

时  间：2024年5月24日8:00

地  点：海韵园实验楼105报告厅

内容摘要:

Rota-Baxter operators on Lie algebras were first studied by Belavin, Drinfeld and Semenov-Tian-Shansky as operator forms of the classical Yang-Baxter equation. As a fundamental tool in studying integrable systems, the factorization theorem of Lie groups by Semenov-Tian-Shansky was obtained by integrating a factorization of Lie algebras from solutions of the modified Yang-Baxter equation. Integrating the Rota-Baxter operators on Lie algebras, we introduce the notion of Rota-Baxter operators on Lie groups and more generally on groups. Then the factorization theorem can be achieved directly on groups. As the underlying structures of Rota-Baxter operators on groups, the notion of post-groups was introduced. The differentiation of post-Lie groups gives post-Lie algebras. Post-groups are also related to braces and Lie-Butcher groups, and give rise to solutions of Yang-Baxter equations. The talk is based on the joint work with Chengming Bai, Li Guo, Honglei Lang and Rong Tang.  

个人简介：

生云鹤，吉林大学数学学院教授，博士生导师,《数学进展》、《J. Nonlinear Math. Phys.》编委，吉林省第十六批享受政府津贴专家（省有突出贡献专家）。2009年1月博士毕业于北京大学，从事Poisson几何、高阶李理论与数学物理的研究，2019年获得国家自然科学基金委优秀青年基金项目，在Math. Ann., CMP, Adv. Math., IMRN等杂志上发表学术论文100余篇，被引用900余次。

 

联系人：王清