Universal envelopes of Malcev Algebras: Pointed Moufang bialgebras

Under study are the pointed unital coassociative cocommutative Moufang $H$-bialgebras. We prove an analog of the Cartier–Kostant–Milnor–Moore theorem for weakly associative Moufang $H$-bialgebras. If the primitive elements commute with group-like elements then these Moufang $H$-bialgebras are isomorphic to the tensor product of a universal enveloping algebra of a Malcev algebra and a loop algebra constructed by a Moufang loop.