On finite-dimensional copointed Hopf algebras over dihedral groups

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 kDm over a dihedral group Dm, with m=4a≥12. 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.