On finite-dimensional copointed Hopf algebras over dihedral groups

Abstract

We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions over a dihedral group D_m, with m=4a> 11. We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups.

arXiv commentThis version: Minor changes, mainly on exposition following referee's advice. To appear in J. Pure Applied Algebra

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• Finite-dimensional Nichols algebras over dual Radford algebras