  We will start from the beginning and define a matroid and its Orlik-Solomon
algebra and holonomy Lie algebra, but first we give some background from
topology and cohomology. A (central) hyperplane arrangement is a finite number
of subspaces of codimension one in a finite dimensional vector space over R, C
or even finite fields. The space X which is the complement of the union of the
hyperplanes has interesting properties. If you consider R^n the cohomology is
however rather trivial, there is just an H^0, since X is a disjoint union of
contractible sets. But it is not a trivial task to compute |H^0|. The way to do
it is to consider the intersection lattice of the hyperplanes and compute its
M\"obius function. The result is that the number of components is the sum of
the absolut values of the M\"obius function (Zaslavsky 1975).
