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 Mat. Sb. (N.S.), 1984, Volume 123(165), Number 2, Pages 212–229 (Mi msb1994)

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

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 207–223

Bibliographic databases:

UDC: 519.4
MSC: 17B10, 17B30, 17B50

Citation: 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
\Bibitem{Dzh84} \by A.~S.~Dzhumadil'daev \paper Irreducible representations of strongly solvable Lie~algebras over a~field of positive characteristic \jour Mat. Sb. (N.S.) \yr 1984 \vol 123(165) \issue 2 \pages 212--229 \mathnet{http://mi.mathnet.ru/msb1994} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=732386} \zmath{https://zbmath.org/?q=an:0569.17004|0542.17004} \transl \jour Math. USSR-Sb. \yr 1985 \vol 51 \issue 1 \pages 207--223 \crossref{https://doi.org/10.1070/SM1985v051n01ABEH002855} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. S. Dzhumadil'daev, “Central extensions of the Zassenhaus algebra and their irreducible representations”, Math. USSR-Sb., 54:2 (1986), 457–474
2. A. S. Dzhumadil'daev, “Generalized Casimir elements”, Math. USSR-Izv., 27:2 (1986), 391–400
3. A. S. Dzhumadil'daev, “On a Levi theorem for Lie algebras of characteristic $p$”, Russian Math. Surveys, 41:5 (1986), 139–140
4. V. V. Panyukov, “Irreducible representations of completely solvable Lie algebras of positive characteristic”, Math. USSR-Izv., 32:3 (1989), 607–626
5. A. S. Dzhumadil'daev, “Cohomology of truncated coinduced representations of Lie algebras of positive characteristic”, Math. USSR-Sb., 66:2 (1990), 461–473
6. 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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