We introduce the concept of comodule Hom-coalgebras and show that comodule Hom-coalgebras can be deformed from comodule coalgebras via endomorphisms. 0
We introduce the conception of matched pairs of (H, β)-Lie algebras, construct an (H, β)-Lie algebra through them. We prove that the cocycle twist of a matched pair of (H, β)-Lie algebras can also be matched.
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 .
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