当前位置: 首 页 - 科学研究 - 学术报告 - 正文

Sino-Russian Mathematics Center-JLU Colloquium(2023-030)—Rota-Baxter operators and coboundary Lie bialgebra structures on perfect finite-dimensional Lie algebras

发表于: 2023-11-22   点击: 

报告题目:Rota-Baxter operators and coboundary Lie bialgebra structures on perfect finite-dimensional Lie algebras

报 告 人:Maxim Goncharov

所在单位:Sobolev Institute of Mathematics

报告时间:2023年12月1日 13:00-14:00

报告地点:313 Zhengxin Building


报告摘要: There is a connection between structures of a Lie bialgebra on a given quadratic Lie algebra L and Rota-Baxter operators of a special type on L. Namely, there is a classical result that says that structures of a triangular Lie bialgebra on a quadratic Lie algebra L are in one-to-one correspondence with skew-symmetric Rota-Baxter operators of weight zero on L. Another classical result states the connection between factorizable Lie bialgebra structures and Rota-Baxter operators of weight 1 satisfying some generalized skew-symmetry property. In this talk, we will generalize these results and speak on the connection between coboundary Lie bialgebra structures on a perfect quadratic Lie algebra with solutions of the modified classical Yang-Baxter equation and Rota-Baxter operators of special type. Also, we will describe the classical double of a coboundary Lie bialgebra in terms of Rota-Baxter operators. As an application, we will speak on coboundary Lie bialgebra structures on simple, semisimple, and reductive finite-dimensional Lie algebras.


报告人简介:Maxim Goncharov, Ph.D., Senior research fellow in Sobolev Institute of Mathematics, Associate Professor at Novosibirsk State University.