Twisted homogeneous racks of type D

FERNANDO FANTINO

Almería

Workshop; Hopf algebras and tensor categories; 2011

Universidad de Almería

The problem of classifying finite-dimensional pointed Hopf algebras over non- abelian finite groups reduces in many cases to a question on conjugacy classes or, more generally, on a (twisted homogeneous) racks and a 2-cocycles. The racks of type D are a distinguished family of racks since they give arise to Nichols algebras of dimension infinite for any cocycle.In this talk, we present some techniques to check when a twisted homogeneous rack (THR) is of type D and present a list of known THR of type D for alternating and sporadic groups.Bibliography[1] N. Andruskiewitsch, G. A. García, F. Fantino and L. Vendramin, On twisted homogeneous racks of type D. Rev. Unión Mat. Argent. 51 No. 2 (2010), 1-16.[2] ------, On Nichols algebras associated to simple racks. Contemp. Math., to appear. Preprint arXiv:1006.5727.[3] F. Fantino and L. Vendramin, On twisted conjugacy classes of type D in sporadic groups. In preparation.