Unified products for Malcev algebras

Abstract

The extending structures and unified products for Malcev algebras are developed. Some special cases of unified products such as crossed products and matched pair of Malcev algebras are studied. It is proved that the extending structures can be classified by some non-abelian cohomology theory. One dimensional flag extending structures of Malcev algebras are also investigated.Add the above two formulas to get the formula (3).Conversely, when w = x in equation (3), it is equation (2).Definition 1.3. Let (M, [ , ]) be a Malcev algebra, a left module of M over a vector space V is a bilinear map ⊲ : M × V → V such that the following condition holds:for all x, y, z ∈ M, q ∈ V .