Year: 2026
Type: preprint
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 $(ρ, θ)$ satisfying compatibility conditions, and provide complete classifications of low-dimensional cases.
Source: arXiv (Cornell University)
Author: Saadaoui, Nejib
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160329882