On racks of type D

F. FANTINO

Oberwolfach

Workshop; Oberwolfach: Nichols Algebras and Weyl Groupoids; 2012

Mathematisches Forschungsinstitut Oberwolfach

Let G be a finite non-abelian group. The study of the classification of finite-dimensional pointed Hopf algebras with group G leads to the study of finite-dimensional Nichols algebras associated with pairs (X,q) where X is a rack an q a 2-cocycle. When the rack is of type D the associated Nichols algebra has infinite dimension for all cocycle.In this talk I will show the present state of the classification of finite simple racks of type D and I will say how this is used to obtain the classification of finite-dimensional pointed Hopf algebras over G for some families of non-abelian (simple) groups.