Constructions Of Rota-Baxter Leibniz Algebras

In this paper,we firstly introduce Rota-Baxter Leibniz algebras,including their con-ceptions,constructions,properties and applications.We mainly focus on their constructions and find some methods to construct them by augment algebras,bialgebras,and weak Hopf algebras.Then we give all the Rota-Baxter operators of weight 0,-1 on low-dimensional nilpotent and solvable Leibniz algebras,respectively.In the end,we introduce an appli-cation of Rota-Baxter Leibniz algebras:Constructing Rota-Baxter 3-Leibniz algebras by Rota-Baxter Leibniz algebras.There are four chapters in this paper:In chapter 1,we introduce the development of Rota-Baxter algebras and Leibniz alge-bras.Then we give the research background,content and main results as well as some basic knowledge of this paper.In chapter 2,we give the definition and constructions of Rota-Baxter Leibniz algebras and some examples to consruct them through agument algebras,bialgebras and weak Hopf algebras.In chapter 3,we introduce the definition of nilpotent and solvable Leibniz algebras.Then wle give all the Rota-Baxter operators of weight 0 and-1 on them with dimensions no more than 3,respectively.In chapter 4,we introduce the conception and some properties of Rota-Baxter 3-Leibniz algebras,then we give a way to construct them by Rota-Baxter Leibniz algebras.