Rota-Baxter Leibniz Algebras and Their Constructions

الملخص EN

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 ≤3, respectively.