Full classification of finite-dimensional Nichols algebras in Yetter–Drinfeld categories over general non-abelian groups

Classify all finite-dimensional Nichols algebras in the Yetter–Drinfeld category over kG for general finite non-abelian groups G, including specifying the permissible supports and braided structures that yield finite-dimensional Nichols algebras.

Background

Despite major advances for abelian groups and several non-abelian families (e.g., rank-two cases and almost diagonal types), a comprehensive classification covering all finite non-abelian groups remains outstanding. Progress hinges on combining Weyl groupoid techniques, rack-cocycle realizations, and structural constraints from group generation by supports.