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Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 4, Pages 735–743 (Mi izv2443)  

This article is cited in 9 scientific papers (total in 9 papers)

On representations of classical semisimple Lie algebras of characteristic $p$

A. N. Rudakov


Abstract: In this paper theorems are proved about the dimension and the structure of irreducible representations of semisimple Lie algebras with nondegenerate Killing form over a field of prime characteristic.

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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:4, 741–749

Bibliographic databases:

UDC: 519.4
MSC: 17B10, 17B20, 22E60
Received: 19.02.1970

Citation: A. N. Rudakov, “On representations of classical semisimple Lie algebras of characteristic $p$”, Izv. Akad. Nauk SSSR Ser. Mat., 34:4 (1970), 735–743; Math. USSR-Izv., 4:4 (1970), 741–749

Citation in format AMSBIB
\Bibitem{Rud70}
\by A.~N.~Rudakov
\paper On representations of classical semisimple Lie algebras of characteristic~$p$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1970
\vol 34
\issue 4
\pages 735--743
\mathnet{http://mi.mathnet.ru/izv2443}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=266970}
\zmath{https://zbmath.org/?q=an:0242.17005}
\transl
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 4
\pages 741--749
\crossref{https://doi.org/10.1070/IM1970v004n04ABEH000929}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. Yu. Weisfeiler, V. G. Kac, “Irreducible representations of Lie $p$-algebras”, Funct. Anal. Appl., 5:2 (1971), 111–117  mathnet  crossref  mathscinet  zmath
    2. V. G. Kats, “O neprivodimykh predstavleniyakh algebr Li klassicheskogo tipa”, UMN, 27:5(167) (1972), 237–238  mathnet  mathscinet  zmath
    3. A. A. Mil'ner, “Irreducible representations of modular Lie algebras”, Math. USSR-Izv., 9:6 (1975), 1169–1187  mathnet  crossref  mathscinet  zmath
    4. Ya. S. Krylyuk, “On the maximal dimension of irreducible representations of simple Lie $p$-algebras of the Cartan series $S$ and $H$”, Math. USSR-Sb., 51:1 (1985), 107–118  mathnet  crossref  mathscinet  zmath
    5. A. N. Panov, “Irreducible representations of the Lie algebra $\mathrm{sl}(n)$ over a field of positive characteristic”, Math. USSR-Sb., 56:1 (1987), 19–32  mathnet  crossref  mathscinet  zmath
    6. Ya. S. Krylyuk, “The Zassenhaus variety of a classical semisimple Lie algebra in finite characteristic”, Math. USSR-Sb., 58:2 (1987), 477–490  mathnet  crossref  mathscinet  zmath
    7. Ya. S. Krylyuk, “On the index of algebras of Cartan type in finite characteristic”, Math. USSR-Izv., 28:2 (1987), 381–399  mathnet  crossref  mathscinet  zmath
    8. Ya. S. Krylyuk, “Indices of standard maximal subalgebras of Cartan-type $p$-algebras of finite characteristic”, Math. USSR-Sb., 67:1 (1990), 1–21  mathnet  crossref  mathscinet  zmath  isi
    9. J.C.arsten Jantzen, “Cartan matrices for restricted Lie algebras”, Math. Z, 2013  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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