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The Lie algebra cohomology of jets

Yunhyong Kim
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Abstract

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.

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Yunhyong Kim. 2003-06-10. The Lie algebra cohomology of jets. https://arxiv.org/abs/math/0208007

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