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arXiv · 2605.02846

Non-abelian extensions of Hom-Jacobi-Jordan algebras

Nejib Saadaoui
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Abstract

This paper develops a cohomology theory for Hom-Jacobi-Jordan algebras using and applies it to classify non-abelian extensions. The main result establishes that equivalence classes of split extensions of a Hom-Jacobi-Jordan algebra $J$ by $V$ are in bijection with the second cohomology group $H^2(J,V)$, generalizing classical results from Lie and Leibniz algebra theory. We characterize extensions explicitly through 2-cocycles $(\rho, \theta)$ satisfying compatibility conditions, and provide complete classifications of low-dimensional cases.

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Nejib Saadaoui. 2026-05-04. Non-abelian extensions of Hom-Jacobi-Jordan algebras. https://arxiv.org/abs/2605.02846

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