A parametric family of simple Lie algebras
Izvestiya. Mathematics , Tome 4 (1970) no. 4, pp. 751-764.

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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 $\varepsilon'$, $\varepsilon\varepsilon'\ne1$.
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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/

[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