Geodesic
Lie algebras with a~subalgebra of codimension~$p$
Izvestiya. Mathematics , Tome 10 (1976) no. 6, pp. 1165-1186.

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All Lie algebras over an algebraically closed field $\mathbf K$, with $\operatorname{char}\mathbf K=p>3$, which have a faithful irreducible representation of degree $p$ are enumerated. Graded Lie algebras $L=\bigoplus^r_{i=-q}L_i$, which have subalgebra $L^-=\bigoplus_{i0}L_i$ with $\operatorname{dim}L^-=p$ are investigated. Simple finite-dimensional modular Lie algebras which have a maximal subalgebra $\mathscr L_0$ of codimension $p>5$ such that for the corresponding noncontractible filtration with $\mathscr L_1\ne0$ the algebra $\operatorname{Gr}\mathscr L$ is transitive are characterized as deformations of such graded algebras. Bibliography: 15 titles. 
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M. I. Kuznetsov. Lie algebras with a~subalgebra of codimension~$p$. Izvestiya. Mathematics , Tome 10 (1976) no. 6, pp. 1165-1186. http://geodesic.mathdoc.fr/item/IM2_1976_10_6_a1/

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