The Classification of Semisimple Hopf Algebras of dimension 16

    Abstract

    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. 

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