Graded Lie algebras of finite characteristic
Izvestiya. Mathematics , Tome 3 (1969) no. 2, pp. 237-304.

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An invariant description is given of finite-dimensional algebras of Cartan type and, with certain restrictions, they are identified with abstract graded Lie algebras defined over algebraically closed fields of characteristic $p>7$.
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A. I. Kostrikin; I. R. Shafarevich. Graded Lie algebras of finite characteristic. Izvestiya. Mathematics , Tome 3 (1969) no. 2, pp. 237-304. http://geodesic.mathdoc.fr/item/IM2_1969_3_2_a0/

[1] Albert A. A., Frank M. S., “Simple Lie algebras of characteristic $p$”, Rend. Torino, 14 (1954–1955), 117–139 | MR

[2] Block R., “New simple Lie algebras of prime characteristic”, Trans. Amer. Math. Soc., 89 (1958), 421–449 | DOI | MR

[3] Block R., “Trace forms of Lie algebras”, Can. J. Math., 14 (1962), 553–564 | MR | Zbl

[4] Cartan E., “Les groupes de transformations continués, infinis, simples”, Ann. Sci. École Norm. Sup., 26 (1909), 93–161 | MR | Zbl

[5] Cartier P., Dualité des variétés abéliennes (10-e année: 1957–1958), Séminaire Bourbaki, 13, Secrétariat mathématique, Paris, 1957–1958 | MR

[6] Chang H. J., “Über Wittsche Lie-Ringe”, Hamb. Abh., 14 (1914), 151–184 | DOI | MR

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

[8] Frank M. S., “A new class of simple Lie algebras”, Proc. Nat. Acad. Sci., 40 (1954), 713–719 | DOI | MR | Zbl

[9] Frank M. S., “Two new classes of simple Lie algebras”, Trans. Amer. Math. Soc., 112 (1964), 456–482 | DOI | MR | Zbl

[10] Freudenthal H., Oktaven, Ausnahmegruppen und Oktavengeometrie, Mathematisch Instituut der Rijksuniversiteit te Utrecht, Utrecht, 1951 | MR

[11] Jacobson N., “Classes of restricted Lie algebras of characteristic $p$. II”, Duke Math. J., 10 (1943), 107–121 | DOI | MR | Zbl

[12] Jacobson N., “A note on three-dimensional simple Lie algebras”, J. Math. and Mech., 7 (1958), 823–831 | MR | Zbl

[13] Kobayashi Sh., Nagano T., “On filtered Lie algebras and geometric structures. I”, J. Math. and Mech., 13 (1964), 875–908 ; “III”, J. Math. and Mech., 14 (1965), 679–706 | MR

[14] Lie S., Gesammelte Abhandlungen, Band VI, Oslo, Leipzig, 1927, 300–365

[15] Ochiai Takushiro, “Classification of the finite nonlinear primitive Lie algebras”, Trans. Amer. Math. Soc., 124:2 (1966), 313–322 | DOI | MR | Zbl

[16] Ree R., “On generalized Witt algebras”, Trans. Amer. Math. Soc., 83 (1956), 510–546 | DOI | MR | Zbl

[17] Singer I. M., Sternberg Sh., “The infinite groups of Lie and Cartan. I.”, J. d'analyse Math., 15:1 (1965), 4–114 | MR

[18] Giiemin V., Shternberg Sh., “Algebraicheskaya model tranzitivnoi differentsialnoi geometrii”, Matematika, 10:4 (1966), 3–31

[19] Dzhekobson N., Algebry Li, Mir, M., 1964 | MR

[20] Klein F., Vysshaya geometriya, GONTI, M., 1939

[21] Kostrikin A. I., Shafarevich I. R., “Psevdogruppy Kartana i $p$-algebry Li”, Dokl. AN SSSR, 168:4 (1966), 740–742 | MR

[22] Kostrikin A. I., “Kvadraty prisoedinennykh endomorfizmov v prostykh $p$-algebrakh Li”, Izv. AN SSSR. Ser. matem., 31 (1967), 445–487 | MR | Zbl

[23] Kostrikin A. I., “Teorema o poluprostykh $p$-algebrakh Li”, Matem. zametki, 2:5 (1967), 465–474 | MR | Zbl

[24] Xodzh V., Pido D., Metody algebraicheskoi geometrii, t. I, IL, M., 1954

[25] Shevalle K., “O nekotorykh prostykh gruppakh”, Matematika, 2:1 (1958), 3–53 | MR