Construction process for simple Lie algebras
Résumé
We give here a construction process for the simple complex Lie algebras and their non Hermitian type real forms which intersect the minimal nilpotent complex adjoint orbit, using a finite dimensional irreducible representation of the conformal group, or of an order 2 covering of it, with highest weight a semi-invariant of degree 4. This semi-invariant is intimately related to the structure of the minimal nilpotent orbit. We also describe a similar construction process for the simple real Lie algebras of Hermitian type.
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