Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras

TL;DR

This paper investigates non-commutative ternary Nambu-Poisson algebras and their Hom-type variants, offering new construction methods, classification results, and exploring twisting principles to generate these algebraic structures.

Contribution

It introduces construction techniques, classification, and twisting principles for non-commutative ternary Nambu-Poisson and Hom-Nambu-Poisson algebras, expanding the understanding of their structure.

Findings

Provided tensor product and direct sum constructions.

Developed twisting principles for algebra generation.

Classified 3-dimensional non-commutative ternary Nambu-Poisson algebras.

Abstract

The main purpose of this paper is to study non-commutative ternary Nambu-Poisson algebras and their Hom-type version. We provide construction results dealing with tensor product and direct sums of two (non-commutative) ternary (Hom-)Nambu-Poisson algebras. Moreover, we explore twisting principle of (non-commutative) ternary Nambu-Poisson algebras along with an algebra morphism that lead to construct (non-commutative) ternary Hom-Nambu-Poisson algebras. Furthermore, we provide examples and a 3-dimensional classification of non-commutative ternary Nambu-Poisson algebras.