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Russian Academy of Sciences. Sbornik. Mathematics, 1995, Volume 80, Issue 1, Pages 15–31
DOI: https://doi.org/10.1070/SM1995v080n01ABEH003512
(Mi sm1011)
 

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

The base rank of varieties of Lie algebras

M. V. Zaicev
References:
Abstract: In this article it is proved that over a field of characteristic zero the product V1,,Vn of varieties of Lie algebras in which Vn is nilpotent has, as a rule, infinite base rank. An exception is the case when n=2, V2 is abelian, and V1 is nilpotent. It is also shown that if V1 is abelian and V2=varsl2, then the base rank of V1V2 is equal to two. A criterion is obtained for the finiteness of the base rank of a special variety. All special varieties of Lie algebras of almost finite base rank are described.
Received: 09.06.1992
Bibliographic databases:
UDC: 512.81
MSC: Primary 17B05, 17B30, 17B70; Secondary 08B99
Language: English
Original paper language: Russian
Citation: M. V. Zaicev, “The base rank of varieties of Lie algebras”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 15–31
Citation in format AMSBIB
\Bibitem{Zai93}
\by M.~V.~Zaicev
\paper The base rank of varieties of Lie algebras
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 80
\issue 1
\pages 15--31
\mathnet{http://mi.mathnet.ru/eng/sm1011}
\crossref{https://doi.org/10.1070/SM1995v080n01ABEH003512}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1257335}
\zmath{https://zbmath.org/?q=an:0819.17006}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995QH35500002}
Linking options:
  • https://www.mathnet.ru/eng/sm1011
  • https://doi.org/10.1070/SM1995v080n01ABEH003512
  • https://www.mathnet.ru/eng/sm/v184/i9/p21
  • This publication is cited in the following 5 articles:
    1. Yuri Bahturin, Alexander A. Mikhalev, Mikhail Zaicev, Handbook of Algebra, 2, 2000, 579  crossref
    2. Zaicev M., “On Regular Varieties of Lie Algebras”, Commun. Algebr., 24:7 (1996), 2455–2462  crossref  mathscinet  zmath  isi
    3. M. V. Zaicev, “Skew-symmetric identities in special Lie algebras”, Sb. Math., 186:1 (1995), 65–77  mathnet  crossref  mathscinet  zmath  isi
    4. M. V. Zaicev, “Standard identity and Capelli identities in Lie algebras”, Russian Math. Surveys, 49:2 (1994), 186–187  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. M. V. Zaicev, “Special Lie algebras”, Russian Math. Surveys, 48:6 (1993), 111–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:359
    Russian version PDF:112
    English version PDF:31
    References:68
    First page:4
     
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