A classification of Nichols algebras of semisimple Yetter–Drinfeld modules over non-abelian groups

Abstract

Over fields of arbitrary characteristic we classify all braid-indecomposable tuples of at least two absolutely simple Yetter–Drinfeld modules over non-abelian groups such that the group is generated by the support of the tuple and the Nichols algebra of the tuple is finite-dimensional. Such tuples are classified in terms of analogs of Dynkin diagrams which encode much information about the Yetter–Drinfeld modules. We also compute the dimensions of these finite-dimensional Nichols algebras. Our proof uses essentially theWeyl groupoid of a tuple of simple Yetter–Drinfeld modules and our previous result on pairs.