A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups

I. HECKENBERGER; L. VENDRAMIN

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

EUROPEAN MATHEMATICAL SOC

Lugar: Zürich; Año: 2017 vol. 19 p. 299 - 356

1435-9855

Over fields of arbitrary characteristic we classify all braid-indecomposabletuples of at least two absolutely simple Yetter-Drinfeld modules overnon-abelian groups such that the group is generated by the support of the tupleand the Nichols algebra of the tuple is finite-dimensional. Such tuples areclassified in terms of analogs of Dynkin diagrams which encode much informationabout the Yetter-Drinfeld modules. We also compute the dimensions of thesefinite-dimensional Nichols algebras. Our proof uses the Weyl groupoid of atuple of simple Yetter-Drinfeld modules.