On Hopf algebras whose coradical is a cocentral abelian cleft extension

Abstract

This paper is a first step toward the full description of a family of Hopf algebras whose coradical is isomorphic to a semisimple Hopf algebra K_{n} obtained by a cocentral abelian cleft extension. We describe the simple Yetter-Drinfeld modules, compute the fusion rules and determine the finite-dimensional Nichols algebras for some of them. In particular, the well-known Fomin-Kirillov algebras appear as Nichols algebras over K_{3}. As a byproduct we obtain new Hopf algebras of dimension 216.Comment: 24 pages. Comments are welcome