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This paper is a first step toward the full description of a family of Hopfalgebras whose coradical is isomorphic to a semisimple Hopf algebra K_{n}obtained by a cocentral abelian cleft extension. We describe the simpleYetter-Drinfeld modules, compute the fusion rules and determine thefinite-dimensional Nichols algebras for some of them. In particular, thewell-known Fomin-Kirillov algebras appear as Nichols algebras over K_{3}. As abyproduct we obtain new Hopf algebras of dimension 216.

On Hopf algebras whose coradical is a cocentral abelian cleft extension