Ternary Leibniz color algebras and beyond

TL;DR

This paper extends the theory of Leibniz algebras to ternary Leibniz color algebras, exploring their structures, examples, and related algebraic systems like Leibniz-Nambu-Poisson color algebras.

Contribution

It introduces the concept of ternary Leibniz color algebras, constructs examples from Leibniz color algebras, and explores their relationships with other algebraic structures.

Findings

Construction methods for ternary Leibniz-Nambu-Poisson color algebras

Relationships between associative trialgebras and tridendriform algebras

Methods for building modules over ternary Leibniz-Nambu-Poisson color algebras

Abstract

The purpose of this paper is to generalize some results on ternary Leibniz algebras to the case of ternary Leibniz color algebras. In particular, we study color Lie triple systems. In order to produce examples of ternary Leibniz color algebras from Leibniz color algebras, several results on Leibniz color algebras are given. Then we introduce and give some constructions of ternary Leibniz-Nambu-Poisson color algebras. The relationship between associative trialgebras and -1- tridendriform algebras are investigated. Moreover, we give some methods of constructing modules over ternary Leibniz-Nambu-Poisson color algebras.