On finite-dimensional copointed Hopf algebras over dihedral groups

TL;DR

This paper classifies all finite-dimensional copointed Hopf algebras over dihedral groups D_m for m>11, using cohomology and lifting methods, resulting in a new infinite family of such algebras.

Contribution

It provides the first complete classification of these Hopf algebras over dihedral groups for m>11, introducing new examples and extending the understanding of their structure.

Findings

Complete classification of copointed Hopf algebras over D_m for m>11

Identification of an infinite family of new examples

Application of cohomology and lifting methods in classification

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.