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Laplacian spectrum for the nilpotent Kac-Moody Lie algebras. (English) Zbl 1255.17011

Summary: 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.

MSC:

17B56 Cohomology of Lie (super)algebras
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
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