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3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shuangjian Guo & Shengxiang Wang & Xiaohui Zhang, 2022. "3-Hom–Lie Yang–Baxter Equation and 3-Hom–Lie Bialgebras," Mathematics, MDPI, vol. 10(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2485-:d:864523
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