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

TL;DR

This paper introduces noncommutative BiHom-pre-Poisson algebras, explores their bimodules and matched pairs, and investigates the relations with BiHom-Poisson algebras using $ ext{O}$-operators.

Contribution

It defines noncommutative BiHom-pre-Poisson algebras and establishes their bimodules, matched pairs, and connections to BiHom-Poisson algebras via $ ext{O}$-operators.

Findings

Defined noncommutative BiHom-pre-Poisson algebras.

Established bimodules and matched pairs for these algebras.

Explored relations between BiHom-Poisson and pre-Poisson algebras using $ ext{O}$-operators.

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 and 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.