Classification of complex simple Lie algebras via projective geometry geometry

Details Classification of complex simple Lie algebras via projective geometry geometry Classification of complex simple Lie algebras via projective geometry geometry

1999-02-17

arxiv.org/abs/math/9902102v2

Mathematics

Algebraic Geometry

slightly revised, to appear in Selecta Mathematica

Scientific paper

We present a new proof of the classification of complex simple Lie algebras via the projective geometry of homogeneous varieties. Our proof proceeds by constructing homogeneous varieties using the ideals of the secant and tangential varieties of homogeneous varieties already constructed. Our algorithms make no reference to root systems. Our proofs use properties of root systems, but not their classification.

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