Classification of complex simple Lie algebras via projective geometry geometry
arXiv:math/9902102
Abstract
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.
slightly revised, to appear in Selecta Mathematica