Geodesic
On the recognition theorem for Lie algebras of characteristic three
Sbornik. Mathematics, Tome 186 (1995) no. 10, pp. 1461-1475

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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. 
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     author = {A. I. Kostrikin and V. V. Ostrik},
     title = {On the recognition theorem for {Lie} algebras of characteristic three},
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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/