Abstract
Let p be a prime, and k be an algebraically closed field of characteristic p. In this paper, we provide the classification of connected Hopf algebras of dimension p3, except for the case when the primitive space of the Hopf algebra is a two-dimensional abelian restricted Lie algebra. Each isomorphism class is presented by generators x, y, z with relations and Hopf algebra structures. Let μ be the multiplicative group of (p2+p−1)-th roots of unity. When the primitive space is one-dimensional and p is odd, there is an infinite family of isomorphism classes, which is naturally parameterized by Ak1/μ.
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