PreprintCC BY-NC-ND 4.0arXiv
Non-abelian extensions of Hom-Jacobi-Jordan algebras
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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BibTeX
@misc{saadaoui2026nonabelian,
title = {{Non-abelian extensions of Hom-Jacobi-Jordan algebras}},
author = {Nejib Saadaoui},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.02846},
eprint = {2605.02846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.02846},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Non-abelian extensions of Hom-Jacobi-Jordan algebras
AU - Nejib Saadaoui
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2605.02846
UR - https://arxiv.org/abs/2605.02846
AB - 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.
ER -