On the classification of simple Lie algebras over a field of nonzero characteristic

V. G. Kac

Izvestiya. Mathematics , Tome 4 (1970) no. 2, pp. 391-413

Résumé

We consider the question of the classification of simple finite-dimensional Lie algebras over an algebraically closed field $K$ of characteristic $p>3$. It is well known that there exist examples of filtrations for which an associative graded Lie algebra $G=\bigoplus\limits_{i\in\mathbf Z}G_i$ has the following properties: a) transitivity; b) $G_0$ is the direct sum of its center and some Lie algebras of the “classical type”, c) the representation of $G_0$ on $G_{-1}$ is irreducible and $p$-represented. The basic result of this paper is the classification of finite-dimensional graded Lie algebras over a field $K$ that satisfy conditions a)–c).