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Keywords = Hom–Leibniz bialgebra

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15 pages, 263 KiB  
Article
The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras
by Shuangjian Guo, Shengxiang Wang and Xiaohui Zhang
Mathematics 2022, 10(11), 1920; https://doi.org/10.3390/math10111920 - 3 Jun 2022
Cited by 1 | Viewed by 1804
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Hopf-Type Algebras, Lie Algebras, Quantum Groups and Related Topics)
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