A classification of Nichols algebras of semi-simple 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 the Weyl groupoid of a tuple of simple Yetter-Drinfeld modules.

61 pages, 4 tables. Final version. Accepted for publication in J. Europ. Math. Soc

References in corpus (3)

• The classification of Nichols algebras over groups with finite root system of rank two
• Root systems and Weyl groupoids for Nichols algebras
• Rank 2 Nichols Algebras of Diagonal Type over Fields of Positive Characteristic

Cited by in corpus (10)

• Rank 2 Nichols Algebras of Diagonal Type over Fields of Positive Characteristic
• Finite dimensional Nichols algebras over Suzuki algebra I: simple Yetter-Drinfeld modules of $A_{N2n}^{\mu \lambda }$
• On Fomin--Kirillov Algebras for Complex Reflection Groups
• Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
• Finite dimensional Nichols algebras over Suzuki algebra II: over simple Yetter-Drinfeld modules of $A_{N2n+1}^{\mu \lambda }$
• Pointed Hopf algebras over non abelian groups with decomposable braidings, I
• Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation
• Generalized nil-Coxeter algebras over discrete complex reflection groups
• On the Tits cone of a Weyl groupoid
• Twist equivalence for Nichols algebras over Coxeter groups