Simple racks of type D and pointed Hopf algebras

F. FANTINO

Tallinn

Conferencia; Quantum: Algebra, Geometry and Information; 2012

Department of Mathematics, Tallinn University of Technology

A fundamental step in the classification of finite-dimensional pointedHopf algebras over non-abelian groups, in the context of the Liftingmethod, is the determination of all finite-dimensional Nichols algebrasof braided vector spaces arising from pairs (X, q), where X is a rack andq is a 2-cocycle. Under certain conditions on X the correspondingNichols algebra is infinite dimensional, and we can discard it in theprevious step. That is the case when X is of type D. In this talk we willpresent some results on the determination of simple racks of type D.This talk is based on a series of articles, mainly on a joint work with L.Vendramin (arXiv:1107.0310).