Geodesic
New methods for the classification of the simple modular Lie algebras
Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 235-245 
H. Strade. New methods for the classification of the simple modular Lie algebras. Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 235-245. http://geodesic.mathdoc.fr/item/SM_1992_71_1_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate the structure of simple modular Lie algebras $L$ over an algebraically closed field of characteristic $p>7$. Let $T$ denote an optimal torus in some $p$-envelope $L_p$. We prove: If $Q(L,T)=L$ and $C_L(T)$ is a Cartan subalgebra, then $L$ is classical. If $Q(L,T)\ne L$ and $C_L(T)$ distinguishes the roots of $T$ on $L/Q(L,T)\ne 0$, then $L$ is of Cartan type. The methods give new proofs even for the restricted simple Lie algebras.

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