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Laplacian spectrum
for the nilpotent Kac–Moody Lie algebras
Dmitry Fuchs and Constance Wilmarth |
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Vol. 247 (2010), No. 2, 323–334
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Abstract |
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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. |
Keywords
Kac–Moody algebras, Laplace operators
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Mathematical Subject Classification 2000
Primary: 17B56, 17B67
Secondary: 81R10
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Milestones
Received: 5 December 2008
Accepted: 2 April 2010
Published: 11 August 2010
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Authors |
| Dmitry Fuchs | |
| Department of Mathematics University of California One Shields Avenue Davis, CA 95616 United States |
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| Constance Wilmarth | |
| Department of Mathematics Northwest Christian University 828 East Eleventh Ave. Eugene, OR 97401 United States |
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