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 <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Fernando FANTINO - Paris,
Titre Nichols algebras and pointed Hopf algebras over non-abelian groups
Horaire14:00 à 15:00
RésumeNichols 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.