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).
(2010).Hom-Lie algebras and Hom-Lie admissible superalgebras.Journal of Alge- bra.324(7): 1513–1528
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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).