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).
(2012).Representations of Hom-Lie algebras.Algebras and Representation Theory15(6): 1081–1098
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Non-abelian extensions of Hom-Jacobi-Jordan algebras
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).