Laplacian spectrum for the nilpotent Kac–Moody Lie algebras

Dmitry Fuchs, Constance Wilmarth
2010 Pacific Journal of Mathematics  
We prove that a maximal nilpotent subalgebra of a Kac-Moody Lie algebra has an (essentially unique) Euclidean metric whose 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.
doi:10.2140/pjm.2010.247.323 fatcat:i3m5ol3vj5eijiy3dtk5jxgeia