$\omega$-Lie algebras

TL;DR

This paper explores a generalization of Lie algebras called $$-Lie algebras, where the Jacobi identity is modified by a skew-symmetric bilinear form, expanding the algebraic structures beyond classical Lie algebras.

Contribution

It introduces and analyzes the structure of $$-Lie algebras, a novel class where the Jacobi identity is replaced by a form-dependent expression.

Findings

Characterization of $$-Lie algebras

Examples illustrating the new structure

Potential applications in algebraic theory

Abstract

We study a certain generalization of Lie algebras where the Jacobian of three elements does not vanish but is equal to an expression depending on a skew-symmetric bilinear form.