BiHom-Poisson color algebras

TL;DR

This paper introduces BiHom-Poisson color algebras, explores their properties, and provides various constructions, including using morphisms, averaging operators, and tensor products, expanding the algebraic framework.

Contribution

It develops the theory of BiHom-Poisson color algebras, including new constructions and their closure properties under specific operators and tensor products.

Findings

BiHom-Poisson color algebras are closed under averaging operators.

Regular BiHom-associative color algebras induce BiHom-Poisson color algebras.

Rota-Baxter operators generate new BiHom-Poisson color algebras.

Abstract

The goal of this paper is to introduce BiHom-Poisson color algebras and give various constructions by using some specific maps such as morphisms. We introduce averaging operator and element of centroid for BiHom-Poisson color algebras and point out that BiHom-Poisson color algebras are closed under averaging operators and elements of centroid. We also show that any regular BiHom-associative color algebra leads to BiHom-Poisson color algebra via the commutator bracket. Then we prove that any BiHom-Poisson color algebra together with Rota-Baxter operator or multiplier give rises to another BiHom-Poisson color algebra. Next, we show that tensor product of any BiHom-associative color algebra and any BiHom-Poisson color algebra is also a BiHom- Poisson color algebra