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Mat. Sb. (N.S.), 1987, Volume 134(176), Number 1(9), Pages 82–92 (Mi msb2650)  

This article is cited in 1 scientific paper (total in 1 paper)

On the algebraic structure of the Lie algebra of vector fields on the line

A. I. Molev


Abstract: The author obtains a description of the structure of a representation of the symmetric group $S_n$ in the space of $n$-linear elements of the variety of Lie algebras generated by the Lie algebra of vector fields on the line. It is proved that this space, as an $S_n$-module, is isomorphic to the space of homogeneous harmonic polynomials of degree $n-1$ in $n$ variables.
Bibliography: 16 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 62:1, 83–94

Bibliographic databases:

UDC: 512.5
MSC: Primary 17B65; Secondary 20C30
Received: 27.08.1986

Citation: A. I. Molev, “On the algebraic structure of the Lie algebra of vector fields on the line”, Mat. Sb. (N.S.), 134(176):1(9) (1987), 82–92; Math. USSR-Sb., 62:1 (1989), 83–94

Citation in format AMSBIB
\Bibitem{Mol87}
\by A.~I.~Molev
\paper On the algebraic structure of the Lie algebra of vector fields on the line
\jour Mat. Sb. (N.S.)
\yr 1987
\vol 134(176)
\issue 1(9)
\pages 82--92
\mathnet{http://mi.mathnet.ru/msb2650}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=912412}
\zmath{https://zbmath.org/?q=an:0663.17010|0638.17006}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 1
\pages 83--94
\crossref{https://doi.org/10.1070/SM1989v062n01ABEH003227}


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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. Kirillov A., “On Identities in Lie-Algebras of Vector-Fields”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1989, no. 2, 11–13  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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