Rota-Baxter Leibniz Algebras and Their Constructions. (2nd December 2018) - Zhang, Liangyun; Li, Linhan; Zheng, Huihui
Abstract : In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight0 and- 1 on solvable and nilpotent Leibniz algebras of dimension≤ 3, respectively.