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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.
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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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http://mi.mathnet.ru/eng/msb2650 http://mi.mathnet.ru/eng/msb/v176/i1/p82
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This publication is cited in the following articles:
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Kirillov A., “On Identities in Lie-Algebras of Vector-Fields”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1989, no. 2, 11–13
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