Bimodules and matched pairs of noncommutative BiHom-(pre)-Poisson algebras

Abstract

The purpose of this paper is to introduce the notion of noncommutative BiHom-pre-Poisson algebra. Also, we establish the bimodules and matched pairs of noncommutative BiHom-(pre)-Poisson algebras. Their related relevant properties are also given. Finally, we exploit the notion of $\mathcal{O}$-operator to illustrate the relations existing between noncommutative BiHom-Poisson and noncommutative BiHom pre-Poisson algebras.