2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64640Let 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.Representation TheoryAlgebraic Topology17B56, 17B65text