Multi-parameter formal deformations of ternary hom-Nambu-Lie algebras

TL;DR

This paper introduces multi-parameter formal deformations for ternary hom-Nambu-Lie algebras, constructing specific deformations of algebraic structures like the Jacobian determinant and cross-product, and relates to the ternary q-Virasoro-Witt algebra.

Contribution

It develops a new framework for multi-parameter deformations of ternary hom-Nambu-Lie algebras and connects them to known algebraic structures.

Findings

Constructed formal deformations of the three-dimensional Jacobian determinant.

Deformed the cross-product in four-dimensional Euclidean space.

Established that the ternary q-Virasoro-Witt algebra is a deformation of the ternary Virasoro-Witt algebra.

Abstract

In this note, we introduce a notion of multi-parameter formal deformations of ternary hom-Nambu-Lie algebras. Within this framework, we construct formal deformations of the three-dimensional Jacobian determinant and of the cross-product in four-dimensional Euclidean space. We also conclude that the previously defined ternary q-Virasoro-Witt algebra is a formal deformation of the ternary Virasoro-Witt algebra.