Pointed Hopf algebras over non abelian groups with decomposable braidings, I

Abstract

We describe all finite-dimensional pointed Hopf algebras whose infinitesimal braiding is a fixed Yetter-Drinfeld module decomposed as the sum of two simple objects: a point and the one of transpositions of the symmetric group in three letters. We give a presentation by generators and relations of the corresponding Nichols algebra and show that Andruskiewitsch-Schneider Conjecture holds for this kind of pointed Hopf algebras.

29 pages

References in corpus (3)

• 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
• Copointed Hopf algebras over ${\mathbb{S}}_4$