Construction process for simple Lie algebras |
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Authors: | Dehbia Achab |
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Institution: | IMJ-Université Pierre et Marie-Curie, 4, Place Jussieu, 75005 Paris, France |
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Abstract: | We give here a construction process for the complex simple Lie algebras and the 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 some two-fold covering of it, with highest weight vector a semi-invariant of degree four. This process leads to a five-graded simple complex Lie algebra and the underlying 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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