Geodesic
Simple modular Lie algebras with a solvable maximal subalgebra
Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 68-76 
M. I. Kuznetsov. Simple modular Lie algebras with a solvable maximal subalgebra. Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 68-76. http://geodesic.mathdoc.fr/item/SM_1976_30_1_a4/
@article{SM_1976_30_1_a4,
     author = {M. I. Kuznetsov},
     title = {Simple modular {Lie} algebras with a~solvable maximal subalgebra},
     journal = {Sbornik. Mathematics},
     pages = {68--76},
     year = {1976},
     volume = {30},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_30_1_a4/}
}
TY  - JOUR
AU  - M. I. Kuznetsov
TI  - Simple modular Lie algebras with a solvable maximal subalgebra
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 68
EP  - 76
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1976_30_1_a4/
LA  - en
ID  - SM_1976_30_1_a4
ER  - 
%0 Journal Article
%A M. I. Kuznetsov
%T Simple modular Lie algebras with a solvable maximal subalgebra
%J Sbornik. Mathematics
%D 1976
%P 68-76
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1976_30_1_a4/
%G en
%F SM_1976_30_1_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper contains a proof of the following Theorem. {\it Let $\mathfrak L$ be a simple Lie algebra which is finite dimensional over an algebraically closed field $K,$ where $\operatorname{char}K=p>3,$ and which contains a solvable maximal subalgebra $\mathfrak L_0$ acting irreducibly on the space $\mathfrak L/\mathfrak L_0$. Then $\mathfrak L$ is either the classical algebra $A_1$ or the Zassenhaus algebra $W_1(n)$.} Bibliography: 10 titles.

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

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

[3] M. Frank, “A new simple Lie algebra of characteristic three”, Proc. Amer. Math. Soc., 38 (1973), 43–46 | DOI | MR | Zbl

[4] N. Dzhekobson, Algebry Li, izd-vo «Mir», Moskva, 1964 | MR

[5] I. Kaplanskii, Algebry Li i lokalno kompaktnye gruppy, izd-vo «Mir», Moskva, 1975

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

[7] R. L. Wilson, “Classification of generalized Witt algebras over algebraically closed fields”, Trans. Amer. Math. Soc., 153 (1971), 191–210 | DOI | MR | Zbl

[8] R. E. Block, “Modules over differential polynomial rings”, Bull. Amer. Math. Soc., 79 (1973), 729–733 | DOI | MR | Zbl

[9] R. L. Wilson, Nonclassical simple Lie algebras, preprint, Yabe Univ., 1969 | MR

[10] R. E. Block, “Determination of the differentiably simple rings with minimal ideal”, Ann. Math. (2), 90 (1969), 433–459 | DOI | MR | Zbl