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Rota-Baxter groups, post-groups and related structures

来源: 03-31

时间:2023-03-31 Fri 17:00-18:30

地点:ZOOM: 815 4690 4797(PW: BIMSA)

组织者:Nicolai Reshetikhin, Andrey Tsiganov, Ivan Sechin

主讲人:Yunhe Sheng (Department of Mathematics, Jilin) University, Changchun, China

Abstract

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 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.

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