Yevgenia Kashina

In previous work, together with Yorck Sommerhäuser, we have constructed a certain family of eight-dimensional semisimple Yetter-Drinfel'd Hopf algebras over the Klein four-group. As every Yetter-Drinfel'd Hopf algebra, these algebras also give rise to ordinary Hopf algebras via the Radford biproduct construction. The arising semisimple Hopf algebra has dimension 32 and therefore can, as every semisimple Hopf algebra of prime power dimension, alternatively be constructed as a Hopf algebra extension. 

We determine all possible ways in which this can be done. In particular, we show that it cannot be constructed as a cocentral abelian extension of prime index. 

We also observe that the set of all possible extensions carries certain symmetries that suggest that the Hopf algebra might be self-dual. 

The talk is based on joint work with Yorck Sommerhäuser, who will give the subsequent talk and will in particular settle the self-duality question.