  Let g be a finite-dimensional complex semi simple Lie algebra. We present a
new calculation of the continuous cohomology of the Lie algebra z g[[z]]. In
particular, we shall give an explicit formula for the Laplacian on the Lie
algebra cochains, from which we can deduce that the cohomology in each
dimension is a finite-dimensional representation of g which contains any
irreducible representation of g at most once.
