Construction and classification of complex simple Lie algebras via projective geometry

Abstract.

We construct the complex simple Lie algebras using elementary algebraic geometry. We use our construction to obtain a new proof of the classification of complex simple Lie algebras that does not appeal to the classification of root systems.

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1. Department of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, U.S.A., e-mail: jml@math.gatech.edu, US

   J. M. Landsberg

2. Institut Fourier, UMR 5582 du CNRS, Université Grenoble I, BP 74, 38402 Saint Martin d'Hères cedex, France, e-mail: Laurent.Manivel@ujf-grenoble.fr, FR

   L. Manivel

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1. J. M. Landsberg
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Landsberg, J., Manivel, L. Construction and classification of complex simple Lie algebras via projective geometry . Sel. math., New ser. 8, 137 (2002). https://doi.org/10.1007/s00029-002-8103-5

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• DOI: https://doi.org/10.1007/s00029-002-8103-5

• Key words. Homogeneous variety, Lie algebra, secant variety.