Classify finite-dimensional pointed Hopf algebras with non-abelian coradical

Classify all finite-dimensional pointed Hopf algebras whose coradical is non-abelian, thereby obtaining a complete result for the non-abelian case analogous to the known classification for abelian coradical.

Background

The introduction reviews the state of the art: finite-dimensional pointed Hopf algebras with abelian coradical have been classified and shown to be cocycle deformations of the associated graded Hopf algebra. However, for non-abelian coradicals the classification remains incomplete.

This problem is central to the broader classification program in Hopf algebra theory and motivates the paper of Nichols algebras over various finite groups, including classical Weyl groups, as a key step toward classifying pointed Hopf algebras with a given group of group-likes.