Title：Rota-Baxter operators and coboundary Lie bialgebra structures on perfect finite-dimensional Lie algebras
Reporter：Maxim Goncharov
Work Unit：Sobolev Institute of Mathematics
Time：Dec.1, 13:00-14:00
Address：313 Zhengxin Building
Summary of the report:
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.
Introduction of the Reporter:
Maxim Goncharov, Ph.D., Senior research fellow in Sobolev Institute of Mathematics, Associate Professor at Novosibirsk State University.
