Finite-dimensional Hopf algebras over the Hopf algebra H:−1,1 of Kashina

Abstract

Let H be the 16-dimensional non-trivial semisimple Hopf algebra H d : − 1 , 1 in the classification work of Kashina [28] . Actually, H ≅ H 8 ⊗ k C 2 , where H 8 is the Kac-Paljutkin algebra [26] . Let V = ⨁ i ∈ I V i , where V i is a simple object in YD H H . All finite-dimensional Nichols algebras satisfying B ( V ) ≅ ⨂ i ∈ I B ( V i ) are determined completely. Under this assumption, we consider and classify all those Hopf algebras of finite-dimensional growth from the semisimple Hopf algebra H d : − 1 , 1 via the relevant Nichols algebras B ( V ) .