Manin triples and quasitriangular structures of Hom-Poisson bialgebras

In this paper, we first introduce the definition of a Hom-Poisson bialgebra and give an equivalent descriptions via the Manin triple of Hom-Poisson algebras. Also we introduce notions of $\mathcal{O}$-operator on a Hom-Poisson algebra, post-Hom-Poisson algebra and quasitriangular Hom-Poisson bialgebra, and present a method to construct post-Hom-Poisson algebras. Finally, we show that a quasitriangular Hom-Poisson bialgebra naturally yields a post-Hom-Poisson algebra.