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

Shuangjian Guo, Shengxiang Wang and Xiaohui Zhang
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Shuangjian Guo: School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
Shengxiang Wang: School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China
Xiaohui Zhang: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2022, vol. 10, issue 11, 1-15

Abstract: 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.

Keywords: Hom–Leibniz bialgebra; Manin triple; relative Rota–Baxter operator; classical Hom–Leibniz Yang–Baxter equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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