  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.

Rings and Algebras