RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1988, Volume 136(178), Number 3(7), Pages 413–425 (Mi msb1751)  

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

On solvable subvarieties of the variety generated by the Witt algebra

S. P. Mishchenko


Abstract: The conjecture that the commutator subalgebra of any solvable algebra lying in the variety generated by the Lie algebra of vector fields on the line is nilpotent is disproved in the case when the ground field has zero characteristic. The algebra constructed turns out to be useful for describing all solvable subvarieties of the variety generated by the Lie algebra of vector fields on the line (it may be regarded as a Witt algebra).
It is proved that any such subvariety either contains this algebra, or consists of algebras with nilpotent commutator subalgebras. An essential role in the proof is played by a result that is of independent interest: a solvable variety consists of algebras with nilpotent commutator subalgebras if and only if all its algebras with degree of nilpotency at most three have this property.
Bibliography: 14 titles.

Full text: PDF file (839 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 415–426

Bibliographic databases:

UDC: 519.4
MSC: Primary 17B05, 17B30, 17A30; Secondary 17B65
Received: 03.06.1986 and 01.12.1987

Citation: S. P. Mishchenko, “On solvable subvarieties of the variety generated by the Witt algebra”, Mat. Sb. (N.S.), 136(178):3(7) (1988), 413–425; Math. USSR-Sb., 64:2 (1989), 415–426

Citation in format AMSBIB
\Bibitem{Mis88}
\by S.~P.~Mishchenko
\paper On solvable subvarieties of the variety generated by the Witt algebra
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 3(7)
\pages 413--425
\mathnet{http://mi.mathnet.ru/msb1751}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=959491}
\zmath{https://zbmath.org/?q=an:0677.17015|0657.17017}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 2
\pages 415--426
\crossref{https://doi.org/10.1070/SM1989v064n02ABEH003317}


Linking options:
  • http://mi.mathnet.ru/eng/msb1751
  • http://mi.mathnet.ru/eng/msb/v178/i3/p413

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. S. P. Mishchenko, “Growth in varieties of Lie algebras”, Russian Math. Surveys, 45:6 (1990), 27–52  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Mishchenko S., “On the Varieties of Resolvable Lie-Algebra”, Dokl. AN SSSR, 313:6 (1990), 1345–1348  mathnet  zmath  isi
    3. S. P. Mishchenko, “On varieties of Lie algebras not containing a three-dimensional simple algebra”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 189–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Mishchenko S., “On the Standard Identity in Solvable Lie-Algebras with Degree of Solvability at Most 3”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1993, no. 5, 63–66  mathscinet  zmath  isi
    5. José A. Freitas, Plamen Koshlukov, Alexei Krasilnikov, “<mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi mathvariant="double-struck">Z</mml:mi></mml:math>-graded identities of the Lie algebra <mml:math altimg="si2.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001”, Journal of Algebra, 427 (2015), 226  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:175
    Full text:61
    References:17

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019