This article is cited in 6 scientific papers (total in 6 papers)
Irreducible representations of strongly solvable Lie algebras over a field of positive characteristic
A. S. Dzhumadil'daev
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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Mathematics of the USSR-Sbornik, 1985, 51:1, 207–223
MSC: 17B10, 17B30, 17B50
A. S. Dzhumadil'daev, “Irreducible representations of strongly solvable Lie algebras over a field of positive characteristic”, Mat. Sb. (N.S.), 123(165):2 (1984), 212–229; Math. USSR-Sb., 51:1 (1985), 207–223
Citation in format AMSBIB
\paper Irreducible representations of strongly solvable Lie~algebras over a~field of positive characteristic
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
A. S. Dzhumadil'daev, “Central extensions of the Zassenhaus algebra and their irreducible representations”, Math. USSR-Sb., 54:2 (1986), 457–474
A. S. Dzhumadil'daev, “Generalized Casimir elements”, Math. USSR-Izv., 27:2 (1986), 391–400
A. S. Dzhumadil'daev, “On a Levi theorem for Lie algebras of characteristic $p$”, Russian Math. Surveys, 41:5 (1986), 139–140
V. V. Panyukov, “Irreducible representations of completely solvable Lie algebras of positive characteristic”, Math. USSR-Izv., 32:3 (1989), 607–626
A. S. Dzhumadil'daev, “Cohomology of truncated coinduced representations of Lie algebras of positive characteristic”, Math. USSR-Sb., 66:2 (1990), 461–473
Jörg Feldvoss, “On the Number of Simple Modules of a Supersolvable Restricted Lie Algebra”, Journal of Algebra, 230:2 (2000), 319
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