Semisimple Hopf algebras of dimension $9q^2$ and high-dimensional semisimple Hopf algebras of Frobenius type

Abstract

Let $k$ be an algebraically closed field of characteristic 0. In this paper, we obtain the structure theorems for semisimple Hopf algebras of dimension $9q^2$ over $k$, where $q$ is a prime number. We also prove that odd-dimensional semisimple Hopf algebras over $k$ of dimension less than 600 are of Frobenius type.