Classification of semisimple Hopf algebras of dimension 16

Yevgenia Kashina

In this paper we completely classify nontrivial semisimple Hopf algebras of dimension $16$. We also compute all the possible structures of the Grothendieck ring of semisimple non-commutative Hopf algebras of dimension $16$. Moreover, we prove that non-commutative semisimple Hopf algebras of dimension $p^{n}$, $p$ is prime, cannot have a cyclic group of grouplikes.