Rota-Baxter groups, post-groups and related structures

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.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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