Low dimensional cocommutative connected Hopf algebras Original Research Article

William M. Singerʹs theory of extensions of connected Hopf algebras is used to give a complete list of the cocommutative connected Hopf algebras over a field of positive characteristic p which have vector space dimension less than or equal to p3. The theory shows that there are exactly two noncommutative nonprimitively generated Hopf algebras on the list, one of which is the Hopf algebra corresponding to the sub-Hopf algebra of the Steenrod algebra generated by P1 and Pp. The commutative Hopf algebras are found using Borelʹs theorem and the primitively generated Hopf algebras using restricted Lie algebras.