Separating invariants for Hopf algebras of small dimensions

In this paper we obtain a finite set S of separating invariants for the variety of Hopf algebras of a fixed dimension. In dimension p(2) where p is a prime or when dimension is < 18, except 8, 12, 16, these invariants determine isomorphism classes of Hopf algebras, i.e., two Hopf algebras of a given dimension are isomorphic if and only if each of the invariants in S take the same values on both the Hopf algebras.