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 $\lt 18$, 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.

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Received 11 November 2018

Accepted 26 October 2019

Published 8 June 2020