Second cohomology group and quadratic extensions of metric Hom-Jacobi–Jordan algebras
Keywords:metric-Hom-Jacobi–Jordan algebra, cohomology, quadratic extension, twofold extension
In this paper, we introduce and study the low dimensional cohomology of metric Hom-Jacobi–Jordan algebras. We establish one-to-one correspondence between the equivalence classes of abelian quadratic
extensions of a Hom-Jacobi–Jordan algebra and its second cohomology group.