Rota-Baxter Leibniz Algebras and Their Constructions. (2nd December 2018)

• Record Type: Journal Article
• Authors: Zhang, Liangyun; Li, Linhan; Zheng, Huihui
• Other Names: Toppan Francesco Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2018(2018)
• Publication Date: 2018-12-02
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2018/8540674
• Languages: English
• ISSNs: 1687-9120

Abstract

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.