Irreducible representations of strongly solvable Lie algebras over a field of positive characteristic

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.