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. 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. We introduce the notion of post-Lie groups, whose differentiations are post-Lie algebras. A Rota-Baxter operator on a group naturally induces a post-group. Post-groups are also closely related to operads, braces, Lie-Butcher groups and various structures.
This video is part of the European Non-Associative Algebra Seminar series.
