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Journal of Lie Theory 14 (2004), No. 1, 271--286
Copyright Heldermann Verlag 2004
The Lie Algebra Cohomology of Jets
Yunhyong Kim
Max-Planck Institut für Mathematik,
Vivatsgasse 7,
53111 Bonn,
Germany,
kimy@mpim-bonn.mpg.de
Let g be a finite-dimensional complex semi-simple 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 finite-dimensional
representation of g which contains any irreducible representation of
g at most once.
MSC: 17B56, 17B65.
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