Non-abelian extensions of Hom-Jacobi-Jordan algebras
Nejib Saadaoui

TL;DR
This paper introduces a cohomology framework for Hom-Jacobi-Jordan algebras, enabling classification of non-abelian extensions via second cohomology groups, generalizing classical algebraic theories.
Contribution
It develops a cohomology theory for Hom-Jacobi-Jordan algebras and classifies non-abelian extensions using second cohomology, extending classical algebraic results.
Findings
Establishes a bijection between split extensions and second cohomology classes.
Provides explicit characterization of extensions through 2-cocycles.
Classifies low-dimensional non-abelian extensions.
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 by are in bijection with the second cohomology group , generalizing classical results from Lie and Leibniz algebra theory. We characterize extensions explicitly through 2-cocycles satisfying compatibility conditions, and provide complete classifications of low-dimensional cases.
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