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

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: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

 间:20245248:00

 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.  

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)。20091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。

 

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