Ternary Leibniz color algebras and beyond

TL;DR

This paper explores the structure and properties of ternary Leibniz color algebras, generalizing existing results, constructing examples, and examining related algebraic systems and their interconnections.

Contribution

It introduces ternary Leibniz color algebras, provides new constructions, and studies their modules, properties, and relationships with other algebraic systems.

Findings

Established constructions of ternary Leibniz color algebras from Leibniz color algebras

Defined bimodules over ternary Leibniz color algebras and their properties

Explored connections among color Lie triple systems, color Jordan triple systems, and Comstrans color algebras

Abstract

The purpose of this paper is to study some Ternary color algebras. We generalize some results on ternary Leibniz algebras to the case of ternary Leibniz color algebras. In order to produce examples of ternary Leibniz color algebras from Leibniz color algebras, several results on Leibniz color algebras are given. Next, We introduce ternary Leibniz color algebras and give some constructions dealing with operators, direct sum and tensor product. After that, We introduce bimodule over ternary Leibniz color algebras and point out that the direct sum and the tensor product of two bimodules over a ternary Leibniz color algebras is also a bimodule over the given ternary Leibniz color algebra. Then, We introduce ternary Leibniz-Poisson color algebras and study some of their properties. Finally, we give a brief description of color Lie triple systems, color Jordan triple systems and Comstrans color algebras. The connections among them are also studied.