Laplacian spectrum for the nilpotent Kac-Moody Lie algebras
- Author(s): Fuchs, Dmitry;
- Wilmarth, Constance
- et al.
Published Web Locationhttps://arxiv.org/pdf/0808.0890.pdf
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.