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Mathematics of the USSR-Izvestiya, 1970, Volume 4, Issue 2, Pages 391–413
DOI: https://doi.org/10.1070/IM1970v004n02ABEH000912
(Mi im2422)
 

This article is cited in 34 scientific papers (total in 34 papers)

On the classification of simple Lie algebras over a field of nonzero characteristic

V. G. Kac
References:
Abstract: We consider the question of the classification of simple finite-dimensional Lie algebras over an algebraically closed field $K$ of characteristic $p>3$. It is well known that there exist examples of filtrations for which an associative graded Lie algebra $G=\bigoplus\limits_{i\in\mathbf Z}G_i$ has the following properties:
a) transitivity;
b) $G_0$ is the direct sum of its center and some Lie algebras of the “classical type”,
c) the representation of $G_0$ on $G_{-1}$ is irreducible and $p$-represented.
The basic result of this paper is the classification of finite-dimensional graded Lie algebras over a field $K$ that satisfy conditions a)–c).
Received: 29.07.1969
Bibliographic databases:
UDC: 519.4
Language: English
Original paper language: Russian
Citation: V. G. Kac, “On the classification of simple Lie algebras over a field of nonzero characteristic”, Math. USSR-Izv., 4:2 (1970), 391–413
Citation in format AMSBIB
\Bibitem{Kac70}
\by V.~G.~Kac
\paper On the classification of simple Lie algebras over a field of nonzero characteristic
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 2
\pages 391--413
\mathnet{http://mi.mathnet.ru//eng/im2422}
\crossref{https://doi.org/10.1070/IM1970v004n02ABEH000912}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=276286}
\zmath{https://zbmath.org/?q=an:0254.17007}
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  • https://doi.org/10.1070/IM1970v004n02ABEH000912
  • https://www.mathnet.ru/eng/im/v34/i2/p385
  • This publication is cited in the following 34 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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