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 Kn
, n an odd positive integer, 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, we give the description of the finite-dimensional Nichols algebras over simple modules over K3. This includes a family of 12-dimensional Nichols algebras depending on 3rd roots of unity. Here,
is isomorphic to the well-known Fomin-Kirillov algebra, and
as graded algebras but
is not isomorphic to
as algebra for
. As a byproduct we obtain new Hopf algebras of dimension 216.
2020 Mathematics Subject Classification: