Rota-Baxter Leibniz algebras and their constructions (Q2425040)

Summary: 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 weight \(0\) and \(-1\) on solvable and nilpotent Leibniz algebras of dimension \(\leq 3\), respectively.