
Journal of Lie Theory 14 (2004), No. 1, 271286 Copyright Heldermann Verlag 2004 The Lie Algebra Cohomology of Jets Yunhyong Kim MaxPlanck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany, kimy@mpimbonn.mpg.de Let g be a finitedimensional complex semisimple Lie algebra. We present a new calculation of the continuous cohomology of the Lie algebra zg[[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 finitedimensional representation of g which contains any irreducible representation of g at most once. MSC: 17B56, 17B65. [ Fulltextpdf (197 KB)] for subscribers only. 