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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,

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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