Geodesic
On the recognition theorem for Lie algebras of characteristic three
Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1461-1475 
A. I. Kostrikin; V. V. Ostrik. On the recognition theorem for Lie algebras of characteristic three. Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1461-1475. http://geodesic.mathdoc.fr/item/SM_1995_186_10_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p=3$ that admit a grading $(L_i;i\geqslant-1)$ of depth 1 are classified in this paper. It is assumed that $L_0$ is a reductive Lie algebra acting irreducibly on $L_{-1}$. Most of the arguments work for any characteristic $p\ne 2$. The case of a non-restricted $L_0$-module $L_{-1}$ was considered previously.

[1] Block R., Wilson R., “The restricted simple Lie algebras are of classical or Cartan type”, Proc. Nat. Acad. Sci. U.S.A., 81 (1984), 5271–5274 | DOI | MR | Zbl

[2] Strade H., Wilson R., “Classification of simple Lie algebras over algebraically closed fields of prime characteristic”, Bull. Amer. Math. Soc., 24 (1991), 357–362 | DOI | MR | Zbl

[3] Kats V. G., “O klassifikatsii prostykh algebr Li nad polem s nenulevoi kharakteristikoi”, Izv. AN SSSR. Ser. matem., 34 (1970), 385–408 | MR | Zbl

[4] Melikyan G. M., “O prostykh algebrakh Li kharakteristiki $5$”, UMN, 35:1 (1980), 203–204 | MR | Zbl

[5] Skryabin S. M., “Novye serii prostykh algebr Li kharakteristiki $3$”, Matem. sb., 183:8 (1992), 3–22 | Zbl

[6] Kuznetsov M. I., “Graded Lie algebras with null component containing sum of commuting ideals”, Commun. Algebra, 12 (1984), 1917–1927 | DOI | MR | Zbl

[7] Benkart G., Kostrikin A. I., Kuznetsov M. I., “The simple graded Lie algebras of characteristic three with classical reductive component $L_0$”, Commun. Algebra (to appear)

[8] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl

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

[10] Serr Zh.-P., Algebry Li i gruppy Li, Mir, M., 1969 | MR | Zbl