2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166546We 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.11 pagesRings and Algebras17B67; 17B56text