Manin triples and quasitriangular structures of Hom-Poisson bialgebras

TL;DR

This paper introduces Hom-Poisson bialgebras, their Manin triple characterization, and constructs quasitriangular structures, establishing a link to post-Hom-Poisson algebras.

Contribution

It defines Hom-Poisson bialgebras, introduces $\\mathcal{O}$-operators, and shows how quasitriangular structures produce post-Hom-Poisson algebras, advancing the theory of Hom-Poisson structures.

Findings

Hom-Poisson bialgebras are characterized via Manin triples.

A method to construct post-Hom-Poisson algebras is provided.

Quasitriangular Hom-Poisson bialgebras induce post-Hom-Poisson algebras.

Abstract

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.