Journal of Lie Theory
Vol. 14, No. 1, pp. 271--286 (2004)
The Lie Algebra Cohomology of Jets
Yunhyong KimYunhyong Kim
Max-Planck Institut für Mathematik
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.