  This is a report on the present state of the problem of determining the
dimension of the Nichols algebra associated to a rack and a cocycle. This is
relevant for the classification of finite-dimensional complex pointed Hopf
algebras whose group of group-likes is non-abelian. We deal mainly with simple
racks. We recall the notion of rack of type D, collect the known lists of
simple racks of type D and include preliminary results for the open cases. This
notion is important because the Nichols algebra associated to a rack of type D
and any cocycle has infinite dimension. For those racks not of type D, the
computation of the cohomology groups is needed. We discuss some techniques for
this problem and compute explicitly the cohomology groups corresponding to some
conjugacy classes in symmetric or alternating groups of low order.
