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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 6, Pages 1224–1247 (Mi izv2258)  

This article is cited in 4 scientific papers (total in 4 papers)

Lie algebras with a subalgebra of codimension $p$

M. I. Kuznetsov


Abstract: All Lie algebras over an algebraically closed field $\mathbf K$, with $\operatorname{char}\mathbf K=p>3$, which have a faithful irreducible representation of degree $p$ are enumerated. Graded Lie algebras $L=\bigoplus^r_{i=-q}L_i$, which have subalgebra $L^-=\bigoplus_{i<0}L_i$ with $\operatorname{dim}L^-=p$ are investigated. Simple finite-dimensional modular Lie algebras which have a maximal subalgebra $\mathscr L_0$ of codimension $p>5$ such that for the corresponding noncontractible filtration with $\mathscr L_1\ne0$ the algebra $\operatorname{Gr}\mathscr L$ is transitive are characterized as deformations of such graded algebras.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:6, 1165–1186

Bibliographic databases:

UDC: 519.4
MSC: Primary 17B05; Secondary 17B10
Received: 19.06.1975

Citation: M. I. Kuznetsov, “Lie algebras with a subalgebra of codimension $p$”, Izv. Akad. Nauk SSSR Ser. Mat., 40:6 (1976), 1224–1247; Math. USSR-Izv., 10:6 (1976), 1165–1186

Citation in format AMSBIB
\Bibitem{Kuz76}
\by M.~I.~Kuznetsov
\paper Lie algebras with a~subalgebra of codimension~$p$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 6
\pages 1224--1247
\mathnet{http://mi.mathnet.ru/izv2258}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=457510}
\zmath{https://zbmath.org/?q=an:0357.17006}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 6
\pages 1165--1186
\crossref{https://doi.org/10.1070/IM1976v010n06ABEH001831}


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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. H. M. Melikyan, “On simple Lie algebras of characteristic $5$”, Russian Math. Surveys, 35:1 (1980), 219–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. I. Kuznetsov, “Graded Lie algebras with zero component equal to a sum of commuting ideals”, Math. USSR-Sb., 44:4 (1983), 511–516  mathnet  crossref  mathscinet  zmath
    3. G. O. Èl'sting, “Cartan extensions of irreducible graded modules over graded Lie algebras”, Russian Math. Surveys, 36:3 (1981), 247–247  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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