Leibniz bialgebras, relative Rota–Baxter operators, and the classical Leibniz Yang–Baxter equation

Journal of noncommutative geometry

article

Rong Tang¹  Yunhe Sheng¹ 

[1] Jilin University

关键词: Leibniz bialgebra;    Rota–Baxter operator;    twilled Leibniz algebra;    classical Leibniz Yang–Baxter equation;   

DOI  :  10.4171/jncg/448

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras, and Leibniz bialgebras are equivalent. Then we introduce the notion of a (relative) Rota–Baxter operator on a Leibniz algebra and construct the graded Lie algebra that characterizes relative Rota–Baxter operators as Maurer–Cartan elements. By these structures and the twisting theory of twilled Leibniz algebras, we further define the classical Leibniz Yang–Baxter equation, classical Leibniz rrr-matrices, and triangular Leibniz bialgebras. Finally, we construct solutions of the classical Leibniz Yang–Baxter equation using relative Rota– Baxter operators and Leibniz-dendriform algebras.

【 授权许可】

CC BY