Color Lie superalgebras and hopf algebras

We give a generalization of the well-known theorem stating that the category of primitively generated Hopf algebras is equivalent to the category of (restricted) Lie algebras. In so doing, instead of Lie algebras, we consider color Lie superalgebras, and instead of a primitively generated Hopf algebra, we take a Hopf algebra H whose semigroup elements form an Abelian group G =G(H), and H is generated by its relatively primitive elements which supercommute with the elements of G. Translated fromAlgebra i Logika, Vol. 34, No. 4, pp. 420–436, July-August, 1995.Supported by the Russian Foundation for Fundamental Research, grant No. 93-01-16171.