Classification of connected Hopf algebras up to prime-cube dimension

Abstract

We classify all connected Hopf algebras up to p^3 dimension over an algebraically closed field of characteristic p>0 under the mild restriction such that in dimension p^3, we only work over odd primes p when the primitive space of these Hopf algebras is a two-dimensional abelian restricted Lie algebra. In a conclusion for any odd prime p, we have two isomorphism classes for the p-dimensional, eight isomorphism classes for the p^2-dimensional and fifty-five isomorphism classes, two finite and nine infinite parametric families for the p^3-dimensional.