Non-abelian extensions of Hom-Jacobi-Jordan algebras

2026/05/04 by Nejib Saadaoui
Mathematics · #math.RA #math.AC

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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 H²(J,V), generalizing classical results from Lie and Leibniz algebra theory. We characterize extensions explicitly through 2-cocycles (ρ, θ) satisfying compatibility conditions, and provide complete classifications of low-dimensional cases.

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