Nichols algebras over groups with finite root system of rank two III

Abstract

We compute the finite-dimensional Nichols algebras over the sum of two simple Yetter-Drinfeld modules V and W over non-abelian quotients of a certain central extension of the dihedral group of eight elements or SL(2,3), and such that the Weyl groupoid of the pair (V,W) is finite. These central extensions appear in the classification of non-elementary finite-dimensional Nichols algebras with finite Weyl groupoid of rank two. We deduce new information on the structure of primitive elements of finite-dimensional Nichols algebras over groups.

30 pages. Title has changed. Final version. Accepted for publication in Journal of Algebra

References in corpus (2)

• Nichols algebras of group type with many quadratic relations
• Nichols algebras over groups with finite root system of rank two II

Cited by in corpus (5)

• A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups
• The classification of Nichols algebras over groups with finite root system of rank two
• Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$
• Nichols algebras over groups with finite root system of rank two II
• Twist equivalence for Nichols algebras over Coxeter groups