Some classifications of finite-dimensional Hopf algebras over Ha:y of Kashina

Abstract

Let [Formula: see text] be the [Formula: see text]-dimensional nontrivial semisimple Hopf algebra [Formula: see text] appeared in Kashina’s work [Classification of semisimple Hopf algebras of dimension 16, J. Algebra 232(2) (2000) 617–663]. We obtain all simple Yetter–Drinfeld modules over [Formula: see text] and then determine all finite-dimensional Nichols algebras satisfying [Formula: see text], where [Formula: see text], each [Formula: see text] is a simple object in [Formula: see text]. Moreover, for Nichols algebras satisfying [Formula: see text], we list some infinite dimensional Nichols algebras [Formula: see text] and obtain finite dimensional Nichols algebras of diagonal type that are either super type or [Formula: see text]. Finally, we describe some liftings of those [Formula: see text] over [Formula: see text].