Geodesic
A parametric family of simple Lie algebras
Izvestiya. Mathematics, Tome 4 (1970) no. 4, pp. 751-764 
A. I. Kostrikin. A parametric family of simple Lie algebras. Izvestiya. Mathematics, Tome 4 (1970) no. 4, pp. 751-764. http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a2/
@article{IM2_1970_4_4_a2,
     author = {A. I. Kostrikin},
     title = {A parametric family of simple {Lie} algebras},
     journal = {Izvestiya. Mathematics},
     pages = {751--764},
     year = {1970},
     volume = {4},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a2/}
}
TY  - JOUR
AU  - A. I. Kostrikin
TI  - A parametric family of simple Lie algebras
JO  - Izvestiya. Mathematics
PY  - 1970
SP  - 751
EP  - 764
VL  - 4
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a2/
LA  - en
ID  - IM2_1970_4_4_a2
ER  - 
%0 Journal Article
%A A. I. Kostrikin
%T A parametric family of simple Lie algebras
%J Izvestiya. Mathematics
%D 1970
%P 751-764
%V 4
%N 4
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_4_a2/
%G en
%F IM2_1970_4_4_a2

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

Over an algebraically closed field $k$ of characteristic $p=3$, a ten-dimensional simple Lie $p$-algebra $L(\varepsilon)$ is constructed which depends only on the parameter $\varepsilon\in k$. It is proved that algebras$L(\varepsilon)$ and $L(\varepsilon')$ are nonisomorphic for distinct values of $\varepsilon$ and $\varepsilon'$, $\varepsilon\varepsilon'\ne1$.

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

[2] Wilson R., “Nonclassical simple Lie algebras”, Bull. Amer. Math. Soc., 75:5 (1969), 987–991 | DOI | MR | Zbl

[3] Kostrikin A. I., Neprivodimye graduirovannye algebry Li s komponentoi $L_0=W_1$, Matem. zametki Uralskogo gos. un-ta, Sverdlovsk, 1970

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

[5] Brown G., “Lie algebras of characteristic three with nondegenerate Killing form”, Trans. Amer. Math. Soc., 137 (1969), 259–268 | DOI | MR | Zbl

[6] Kaplansky I., “Lie algebras of characteristic $p$”, Trans. Amer. Math. Soc., 89 (1958), 149–183 | DOI | MR | Zbl

[7] Rudakov A. N., Shafarevich I. R., “Neprivodimye predstavleniya prostoi trekhmernoi algebry Li nad polem konechnoi kharakteristiki”, Matem. zametki, 2:5 (1967), 439–454 | MR | Zbl