Algebraic constructions for Jacobi-Jordan algebras

For a given Jacobi-Jordan algebra A and vector space V over field k , non-abelian cohomological type object H 2 ( ) is constructed: it classifies all algebras containing as subalgebra of codimension equal to dim . Any such isomorphic so-called unified product ♮ Furthermore, we introduce the bicrossed (semi-direct, crossed, or skew crossed) ⋈ associated two special case product. Several examples applications are provided: Galois group extension ⊆ described subgroup semidirect groups GL ⋊ Hom an Artin theorem for proven.