Kupershmidt operators on $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras structures

TL;DR

This paper introduces noncommutative 3-BiHom-Poisson color algebras, explores their representations and Kupershmidt operators, and investigates their relationship with 3-BiHom-pre-Poisson color algebras.

Contribution

It defines a new class of noncommutative 3-BiHom-Poisson color algebras and studies their structure, representations, and connections to pre-Poisson algebras via Kupershmidt operators.

Findings

Defined noncommutative 3-BiHom-Poisson color algebras.

Established Kupershmidt operators on these algebras.

Linked 3-BiHom-Poisson and pre-Poisson structures.

Abstract

The purpose of this paper is to introduce the class of noncommutative $3$-BiHom-Poisson color algebras, which is a combination of $3$-BiHom-Lie color algebras and BiHom-associative color algebras under a compatibility condition, called BiHom-Leibniz color identity, and then study their representations and associated Kupershmidt operators. In addition, we introduce the notion of noncommutative $3$-BiHom-pre-Poisson color algebras and investigate the relationship between noncommutative $3$-BiHom-Poisson color algebras and $3$-BiHom-pre-Poisson color algebras via Kupershmidt operators.