The constructions of 3-Hom-Lie bialgebras

Abstract

In this paper, we first introduce the notion of a 3-Hom-Lie bialgebra and prove that it is equivalent to a Manin triple of 3-Hom-Lie algebras. Also, we study the $\mathcal{O}$-operator and construct solutions of the 3-Lie classical Hom-Yang-Baxter equation interms of $\mathcal{O}$-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.

arXiv comment17pages. arXiv admin note: text overlap with arXiv:1304.7334, arXiv:1604.05996, arXiv:1711.08381 by other authors

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