Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 1, pp. 271--286 (2004)

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The Lie Algebra Cohomology of Jets

Yunhyong Kim

Yunhyong Kim
Max-Planck Institut für Mathematik
Vivatsgasse 7
D-53111 Bonn

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.

Classification (MSC2000): 17B56; 17B65

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Electronic version published on: 29 Jan 2004. This page was last modified: 1 Sep 2004.

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