Finite-dimensional Hopf Algebras Over The Kashina Hopf Algebras

Kashina[52]classified the 16-dimensional nontrivial(namely,noncommutative and noncocommutative)semisimple Hopf algebra and there are 16 semisimple Hopf algebras.In this thesis,3 nontrivial semisimple Hopf algebras(Hb:1 and its dual,Hd:-1,1)are studied as follows:Let H be one of them.First,We obtain all simple Yetter-Drinfeld modules over H and then determine all finite-dimensional Nichols algebras satisfying(?)7 where V=?i?IVi?each Vi is a simple object in;HHYD.Finally,we describe all liftings of those B(V)over H.