Non-abelian extensions of Hom-Jacobi-Jordan algebras
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911644801564672 |
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| author | Saadaoui, Nejib |
| author_facet | Saadaoui, Nejib |
| contents | 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 $(ρ, θ)$ satisfying compatibility conditions, and provide complete classifications of low-dimensional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02846 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-abelian extensions of Hom-Jacobi-Jordan algebras Saadaoui, Nejib Rings and Algebras Commutative Algebra 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 $(ρ, θ)$ satisfying compatibility conditions, and provide complete classifications of low-dimensional cases. |
| title | Non-abelian extensions of Hom-Jacobi-Jordan algebras |
| topic | Rings and Algebras Commutative Algebra |
| url | https://arxiv.org/abs/2605.02846 |