Geodesic
On the classification of simple Lie algebras over a field of nonzero characteristic
Izvestiya. Mathematics, Tome 4 (1970) no. 2, pp. 391-413 
V. G. Kac. On the classification of simple Lie algebras over a field of nonzero characteristic. Izvestiya. Mathematics, Tome 4 (1970) no. 2, pp. 391-413. http://geodesic.mathdoc.fr/item/IM2_1970_4_2_a7/
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     author = {V. G. Kac},
     title = {On the classification of simple {Lie} algebras over a field of nonzero characteristic},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the question of the classification of simple finite-dimensional Lie algebras over an algebraically closed field $K$ of characteristic $p>3$. It is well known that there exist examples of filtrations for which an associative graded Lie algebra $G=\bigoplus\limits_{i\in\mathbf Z}G_i$ has the following properties: a) transitivity; b) $G_0$ is the direct sum of its center and some Lie algebras of the “classical type”, c) the representation of $G_0$ on $G_{-1}$ is irreducible and $p$-represented. The basic result of this paper is the classification of finite-dimensional graded Lie algebras over a field $K$ that satisfy conditions a)–c).

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