Abstract: We introduce the notion of post-groups, which are the underlying structures of Rota-Baxter operators on groups. 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 set-theoretical solutions of Yang-Baxter equations. We further introduce the notion of post-groupoids, whose differentiations are post-Lie algebroids. We show that post-groupoids give quiver-theoretical solutions of the Yang-Baxter equation on the underlying quiver of the subadjacent groupoids.
The talk is based on the joint work with Chengming Bai, Li Guo, Rong Tang and Chenchang Zhu.
Bio: Yunhe Sheng is a Professor in Jilin University. He received his Ph. D degree from Peking University in 2009, and then spent one year in Goettingen University as a post-doctor. His research interests are Poisson geometry, higher Lie theory and mathematical physics.
