  A complex hypersurface D in complex affine n-space C^n is a linear free
divisor (LFD) if its module of logarithmic vector fields has a global basis of
linear vector fields. We classify all LFDs for n at most 4.
  Analogous to Grothendieck's comparison theorem, we say that the global
logarithmic comparison theorem (GLCT) holds for D if the complex of global
logarithmic differential forms computes the complex cohomology of the
complement of D in C^n. We develop a general criterion for the GLCT for LFDs
and prove that it is fulfilled whenever the Lie algebra of linear logarithmic
vector fields is reductive. For n at most 4, we show that the GLCT holds for
all LFDs.
  We show that LFDs arising naturally as discriminants in quiver representation
spaces (of real Schur roots) fulfill the GLCT. As a by-product we obtain a
simplified proof of a theorem of V. Kac on the number of irreducible components
of such discriminants.
