Ternary Leibniz color algebras and beyond

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.