Geodesic
On the classification of simple Lie algebras over a field of nonzero characteristic
Izvestiya. Mathematics, Tome 4 (1970) no. 2, pp. 391-413 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {On the classification of simple {Lie} algebras over a field of nonzero characteristic},
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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/

[1] Veisfeiler B. Yu., “Beskonechnomernye filtrovannye algebry Li i ikh svyaz s graduirovannymi algebrami Li”, Funkts. analiz., 2:1 (1968), 94–95 | MR | Zbl

[2] Dzhekobson N., Algebry Li, M., 1964

[3] Kats V. G., “Prostye neprivodimye graduirovannye algebry Li konechnogo rosta”, Izv. AN SSSR. Ser. matem., 32 (1968), 1323–1367 | Zbl

[4] Kats V. G., “Nekotorye svoistva kontragredientnykh algebr Li”, Trudy MIEM, 1970, no. 5, 48–59

[5] Kostrikin A. I., Shafarevich I. R., “Graduirovannye algebry Li konechnoi kharakteristiki”, Izv. AN SSSR. Ser. matem., 33 (1969), 251–322 | MR | Zbl

[6] Curtis C., “Representation of Lie algebras of classical type with application to linear groups”, J. Math. and mech., 9 (1960), 307–326 | MR | Zbl

[7] Seligman G. B., “Some results in Lie $p$-algebras”, Bull. Amer. Math. Soc., 73:4 (1967), 528–530 | DOI | MR | Zbl