On finite-dimensional copointed Hopf algebras over dihedral groups
Let \(k\) be an algebraically closed field of characteristic zero, and denote by \(\mathbb{D}_m\) the dihedral group of order \(2m\) for any \(m\geq 3\). The aim of the paper is to classify the finite dimensional Hopf algebras with coradical \((k\mathbb{D}_m)^*\), the dual of the group Hopf algebra of \(\mathbb{D}_m\), for \(m=4a\geq 12\). The approach uses the lifting method, which is very efficient for classifying Hopf algebras with coradical a Hopf subalgebra, deformation theory and some cohomological methods for classifying the liftings.
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