## The Classification of Semisimple Hopf Algebras of dimension 16

Venue: | J. of Algebra |

Citations: | 13 - 1 self |

### BibTeX

@ARTICLE{Kashina_theclassification,

author = {Yevgenia Kashina},

title = {The Classification of Semisimple Hopf Algebras of dimension 16},

journal = {J. of Algebra},

year = {}

}

### OpenURL

### Abstract

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. 1. Introduction. Recently various classification results were obtained for finite-dimensional semisimple Hopf algebras over an algebraically closed field of characteristic 0. The smallest dimension, for which the question was still open, was 16. In this paper we completely classify all nontrivial (i.e. noncommutative and non-cocommutative) Hopf algebras of dimension 16. Moreover, we consider all