# Séminaires : Séminaire d'Algèbre

 Equipe(s) : gr, Responsables : J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud. Email des responsables : Jacques Alev , David Hernandez , Bernhard Keller , Thierry Levasseur , Sophie Morier-Genoud Salle : 001 Adresse : IHP Description

 Orateur(s) Fernando FANTINO - Paris, Titre Nichols algebras and pointed Hopf algebras over non-abelian groups Date 26/11/2012 Horaire 14:00 à 15:00 Résume Nichols algebras play a crucial rôle in the classification of finite-dimensional complex pointed Hopf algebras in the context of Lifting method given by Andruskiewitsch and Schneider. These authors have obtained the 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-abelian case. I will describe a strategy to approach the classification by means of Nichols algebras coming from a rack and a 2-cocycle. I will show some criteria to decide the dimension of these Nichols algebras and I will presented a list of the results obtained for some families of non-abelian groups. [1] N. Andruskiewitsch, F. Fantino, M. Graña and L. Vendramin, Finite-dimensional pointed Hopf algebras with alternating groups are trivial'', Ann. Mat. Pura Appl. (4) 190 2 (2011) 225-245. [2] N. Andruskiewitsch, F. Fantino, M. Graña and L. Vendramin, Pointed Hopf algebras over the sporadic simple groups'', J. Algebra 325 1 (2011) 305-320. [3] F. Fantino and G. A. García, On pointed Hopf algebras over dihedral groups'', Pacific J. Math., 252 1 (2011), 69-91. Salle 001 Adresse IHP