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Mat. Sb., 1995, Volume 186, Number 1, Pages 65–78 (Mi msb4)  

This article is cited in 2 scientific papers (total in 2 papers)

Skew-symmetric identities in special Lie algebras

M. V. Zaicev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper we study the connection between a standard Lie identity and Capelli identities in Lie algebras over a field of characteristic zero. It is shown that the standard identity of degree eight implies all Capelli identities in special Lie algebras, while this is false for degree nine. It is further shown that all Capelli identities follow from a standard identity in a product of two nilpotent varieties provided that the right-hand factor is of class at most two; and that, for $n\geqslant 2$, the Lie algebra $W_n$ satisfies an identity not following from a standard identity.

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English version:
Sbornik: Mathematics, 1995, 186:1, 65–77

Bibliographic databases:

UDC: 512
MSC: Primary 17B01; Secondary 17B65
Received: 12.04.1994

Citation: M. V. Zaicev, “Skew-symmetric identities in special Lie algebras”, Mat. Sb., 186:1 (1995), 65–78; Sb. Math., 186:1 (1995), 65–77

Citation in format AMSBIB
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\by M.~V.~Zaicev
\paper Skew-symmetric identities in special Lie algebras
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 1
\pages 65--78
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1641672}
\zmath{https://zbmath.org/?q=an:0855.17002}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 1
\pages 65--77
\crossref{https://doi.org/10.1070/SM1995v186n01ABEH000004}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ91900004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Zaitsev, “A superrank of varieties of Lie algebras”, Algebr Logic, 37:4 (1998), 223  crossref  mathscinet  zmath
    2. Vladimir Yu Protasov, “Invariant functions for the Lyapunov exponents of random matrices”, Sb. Math, 202:1 (2011), 101  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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