  For W a finite (2-)reflection group and B its (generalized) braid group, we
determine the Zariski closure of the image of B inside the corresponding
Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and
generated in the group algebra of W by the reflections of W. We determine its
decomposition in simple factors. In case W is a Coxeter group, we prove that
the representations involved are unitarizable when the parameters of the
representations have modulus 1 and are close to 1. We consequently determine
the topological closure in this case.
