Laplacian spectrum for the nilpotent Kac-Moody Lie algebras
  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. 
Dmitry Fuchs, Constance Wilmarth