The Classical Hom-Leibniz Yang-Baxter Equation and Hom-Leibniz Bialgebras

被引：1

作者：

Guo, Shuangjian ^{[1
]}

Wang, Shengxiang ^{[2
]}

Zhang, Xiaohui ^{[3
]}

机构：

[1] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China

[2] Chuzhou Univ, Sch Math & Finance, Chuzhou 239000, Peoples R China

[3] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

MATHEMATICS | 2022年 / 10卷 / 11期

关键词：

Hom-Leibniz bialgebra; Manin triple; relative Rota-Baxter operator; classical Hom-Leibniz Yang-Baxter equation; LIE-ALGEBRAS;

D O I：

10.3390/math10111920

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first introduce the notion of Hom-Leibniz bialgebras, which is equivalent to matched pairs of Hom-Leibniz algebras and Manin triples of Hom-Leibniz algebras. Additionally, we extend the notion of relative Rota-Baxter operators to Hom-Leibniz algebras and prove that there is a Hom-pre-Leibniz algebra structure on Hom-Leibniz algebras that have a relative Rota-Baxter operator. Finally, we study the classical Hom-Leibniz Yang-Baxter equation on Hom-Leibniz algebras and present its connection with the relative Rota-Baxter operator.

引用

页数：15

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