Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras

TL;DR

This paper introduces a method to construct ternary Hom-Nambu-Lie algebras from binary Hom-Lie algebras using trace functions and twisting maps, highlighting the importance of kernel positions.

Contribution

It presents a novel construction of ternary Hom-Nambu-Lie algebras from Hom-Lie algebras, emphasizing the role of kernels of twisting maps and trace functions.

Findings

Construction method for ternary Hom-Nambu-Lie algebras from Hom-Lie algebras

Role of kernels of twisting maps and trace functions in algebra structure

Examples demonstrating the new construction approach

Abstract

The purpose of this paper is to investigate ternary multiplications constructed from a binary multiplication, linear twisting maps and a trace function. We provide a construction of ternary Hom-Nambu and Hom-Nambu-Lie algebras starting from a binary multiplication of a Hom-Lie algebra and a trace function satisfying certain compatibility conditions involving twisting maps. We show that mutual position of kernels of twisting maps and the trace play important role in this context, and provide examples of Hom-Nambu-Lie algebras obtained using this construction.