Laplacian spectrum for the nilpotent Kac-Moody Lie algebras

Details Laplacian spectrum for the nilpotent Kac-Moody Lie algebras Laplacian spectrum for the nilpotent Kac-Moody Lie algebras

2008-08-06

arxiv.org/abs/0808.0890v1

Mathematics

Rings and Algebras

11 pages

Scientific paper

We prove that the maximal nilpotent subalgebra of a Kac-Moody Lie algebra has
an (essentially unique) Euclidean metric with respect to which the Laplace
operator in the chain complex is scalar on each component of a given degree.
Moreover, both the Lie algebra structure and the metric are uniquely determined
by this property.

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