3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie 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 14, 1-17

Abstract: In this paper, we first introduce the notion of a 3-Hom–Lie bialgebra and give an equivalent description of the 3-Hom–Lie bialgebras, the matched pairs and the Manin triples of 3-Hom–Lie algebras. In addition, we define O -operators of 3-Hom–Lie algebras and construct solutions of the 3-Hom–Lie Yang–Baxter equation in terms of O -operators and 3-Hom–pre-Lie algebras. Finally, we show that a 3-Hom–Lie algebra has a phase space if and only if it is sub-adjacent to a 3-Hom–pre-Lie algebra.

Keywords: 3-Hom–Lie algebra; Manin triple; matched pair; symplectic structure; representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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