報告題目：Rota-Baxter groups, post-groups and related structures

報告人： 生雲鶴 教授

單 位： 吉林大學

報告時間：4月12日 10:00-11:00(周三上午)

騰訊會議：911-336-472

報告摘要：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.

報告人簡介：生雲鶴，吉林大學教授，《數學進展》、《J. Nonlinear Math. Phys.》編委，吉林省第十六批享受政府津貼專家（省有突出貢獻專家）。2009年1月博士畢業于北京大學，從事Poisson幾何、高階李理論與數學物理的研究，2019年獲得國家自然科學基金委優秀青年基金項目，在Math. Ann., CMP, Adv. Math., Tran. AMS, IMRN, JNCG, JA等雜志上發表學術論文80餘篇，被引用600餘次。

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