Nichols algebras and pointed Hopf algebras over non-abelian groups

FERNANDO FANTINO

Clermont-Ferrand

Seminario; Séminaire del Geometrie, algebre, algebres d'operateurs; 2011

Laboratoire de Mathématiques (UMR 6620), Université Blaise Pascal

Nichols algebras play a crucial role in the classification of finite-dimensional complex pointed Hopf algebras in the context of LiftingMethod given by Andruskiewitsch and Schneider. These authors have obtainedthe classification when the group-likes form an abelian group whose order is relatively prime to 210 (´05). This talk is based on a series of articles concerned with the non-abeliancase. I will describe Nichols algebras B coming from a rack and a 2-cocycle,I will show some criteria to decide the dimension of B and I will presenteda list of results obtained for different families of non-abelian groups.