One solution of the 3D Jacobi identities allows determining an infinity of them

TL;DR

The paper shows that knowing one solution to the 3D Jacobi identities enables the explicit construction of infinitely many new solutions, expanding understanding of these algebraic structures.

Contribution

It introduces a method to generate infinite solutions of 3D Jacobi identities from a single known solution, providing explicit constructions and examples.

Findings

Infinite families of solutions can be derived from one known solution.

Explicit formulas for new solutions are provided.

Examples illustrate the method's effectiveness.

Abstract

It is demonstrated that the knowledge of a single and arbitrary solution of the three-dimension\-al Jacobi equations allows determining infinite families of new solutions, which are generally and explicitly constructed in what follows. Examples are given.