Geodesic
Irreducible representations of strongly solvable Lie~algebras over a~field of positive characteristic
Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 207-223

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It is proved that for any modular Lie algebra there exists a unique (to within an isomorphism) $p$-hull of minimal dimension. It is shown that the classes of strongly solvable and completely solvable Lie algebras coincide. It is proved that an irreducible representation of a strongly solvable Lie algebra is monomial, and a formula for the dimension of the representation in terms of the derivation algebra and its stationary subalgebra is obtained. The irreducible representations of the maximal (solvable and nilpotent) subalgebras of a Zassenhaus algebra with basic weights are described. Bibliography: 17 titles. 
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     author = {A. S. Dzhumadil'daev},
     title = {Irreducible representations of strongly solvable {Lie~algebras} over a~field of positive characteristic},
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A. S. Dzhumadil'daev. Irreducible representations of strongly solvable Lie~algebras over a~field of positive characteristic. Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 207-223. http://geodesic.mathdoc.fr/item/SM_1985_51_1_a12/