
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.
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