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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 4(12), Pages 568–574 (Mi msb2485)  

This article is cited in 5 scientific papers (total in 5 papers)

Graded Lie algebras with zero component equal to a sum of commuting ideals

M. I. Kuznetsov


Abstract: This paper considers transitive irreducible 1-graded Lie algebras $L=\bigoplus_{i\geqslant-1}L_i$, $L_1=0$, over an algebraically closed field $K$ of characteristic $p\geqslant0$, $p\ne2$. We prove that if $L_0=G_1+…+G_s$, $G_i\ne Z(L_0)$, is the decomposition of $L_0$ and the ideals of $G_i$ commute, then $s=1$ or $s=2$. In the latter case $L$ is isomorphic to one of the algebras $A_n$, $A^z_{n_0p-1}$ or $\widetilde{\mathfrak{gl}}(n_0p)=\mathfrak{gl}(n_0p)/\langle1\rangle$. .
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 44:4, 511–516

Bibliographic databases:

UDC: 519.4
MSC: 17B70, 17B05, 17B50
Received: 03.03.1981

Citation: M. I. Kuznetsov, “Graded Lie algebras with zero component equal to a sum of commuting ideals”, Mat. Sb. (N.S.), 116(158):4(12) (1981), 568–574; Math. USSR-Sb., 44:4 (1983), 511–516

Citation in format AMSBIB
\Bibitem{Kuz81}
\by M.~I.~Kuznetsov
\paper Graded Lie algebras with zero component equal to a~sum of commuting ideals
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 4(12)
\pages 568--574
\mathnet{http://mi.mathnet.ru/msb2485}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=665857}
\zmath{https://zbmath.org/?q=an:0506.17006|0486.17005}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 4
\pages 511--516
\crossref{https://doi.org/10.1070/SM1983v044n04ABEH000983}


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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. Kuznetsov M., “Graded Lie-Algebras with Null Component Containing Sum of Commuting Ideals”, Commun. Algebr., 12:15-1 (1984), 1917–1927  crossref  mathscinet  zmath  isi
    2. M. I. Kuznetsov, “Classification of simple graded Lie algebras with nonsemisimple component $L_0$”, Math. USSR-Sb., 66:1 (1990), 145–158  mathnet  crossref  mathscinet  zmath  isi
    3. Ostrik V., “2-Grading Lie Algebras of the Characteristic 3”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1999, no. 1, 54–55  mathscinet  zmath  isi
    4. Gregory T. Kuznetsov M., “On Depth-Three Graded Lie Algebras of Characteristic Three with Classical Reductive Null Component”, Commun. Algebr., 32:9 (2004), 3339–3371  crossref  mathscinet  zmath  isi
    5. M. I. Kuznetsov, “Graded Lie algebras with null component contained in a sum of commuting algebras”, J. Math. Sci., 164:2 (2010), 250–254  mathnet  crossref  mathscinet  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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