Nichols algebras and pointed Hopf algebras over non-abelian groups

F. FANTINO

Paris

Seminario; Séminaire d'algèbre (Institut Henri Poincaré); 2012

Institut de Mathématiques de Jussieu et Institut Henri Poincaré

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.