ON SEMISIMPLE HOPF ALGEBRAS OF DIMENSION 2^{n}

YEVGENIA KASHINA

Abstract. In this paper we classify all nontrivial semisimple Hopf algebras of dimension 2^{n+1} with the group of grouplikes isomorphic to ℤ_{2^{n−1}} × ℤ_{2}. Moreover, we extend some results on irreducible representations from groups to semisimple Hopf algebras and prove that certain semisimple Hopf algebras, including the ones classified in this paper, satisfy the generalized power map property.