Finite-dimensional Hopf algebras over the Hopf algebra Hb:1 of Kashina

Abstract Let H be the 16-dimensional nontrivial semisimple Hopf algebra H b : 1 appeared in Kashina's work [32] . We obtain all simple Yetter-Drinfeld modules over H and then determine all finite-dimensional Nichols algebras satisfying B ( V ) ≅ ⨂ i ∈ I B ( V i ) , where V = ⨁ i ∈ I V i , each V i is a simple object in YD H H . Finally, we describe all liftings of those B ( V ) over H.