Matematicheskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
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., 1989, Volume 180, Number 6, Pages 798–808 (Mi msb1635)  

This article is cited in 4 scientific papers (total in 4 papers)

Locally representable varieties of Lie algebras

M. V. Zaicev


Abstract: A description is obtained for locally representable varieties of Lie algebras, i.e., varieties in which an arbitrary finitely generated algebra has a faithful representation of finite dimension over an extension of the ground field. In the case of an infinite field $\Phi$ a variety $V$ of Lie algebras is locally representable if and only if the following two conditions hold:
1) $zy^nx=\sum\limits_{j=1}^n\alpha_jy^jzy^{n-j}x$ is an identity in $V$ for some $\alpha_1,…,\alpha_n$ in $\Phi$; and
2) an arbitrary finitely generated algebra in $V$ lies in a product $N_cN_d$ of nilpotent varieties, where $d=1$ if $\operatorname{char}\Phi=0$.
Bibliography: 13 titles.

Full text: PDF file (716 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1990, 67:1, 249–259

Bibliographic databases:

UDC: 512
MSC: Primary 17B65, 08B99; Secondary 17B15, 17B30, 17B35, 17B40
Received: 19.01.1988 and 15.09.1988

Citation: M. V. Zaicev, “Locally representable varieties of Lie algebras”, Mat. Sb., 180:6 (1989), 798–808; Math. USSR-Sb., 67:1 (1990), 249–259

Citation in format AMSBIB
\Bibitem{Zai89}
\by M.~V.~Zaicev
\paper Locally representable varieties of Lie~algebras
\jour Mat. Sb.
\yr 1989
\vol 180
\issue 6
\pages 798--808
\mathnet{http://mi.mathnet.ru/msb1635}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1015041}
\zmath{https://zbmath.org/?q=an:0688.17004|0699.17013}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 1
\pages 249--259
\crossref{https://doi.org/10.1070/SM1990v067n01ABEH002087}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990ED88000015}


Linking options:
  • http://mi.mathnet.ru/eng/msb1635
  • http://mi.mathnet.ru/eng/msb/v180/i6/p798

    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. M. V. Zaicev, “Special Lie algebras”, Russian Math. Surveys, 48:6 (1993), 111–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. K. A. Zubrilin, “O klasse nilpotentnosti prepyatstviya dlya predstavimosti algebr, udovletvoryayuschikh tozhdestvam Kapelli”, Fundament. i prikl. matem., 1:2 (1995), 409–430  mathnet  mathscinet  zmath
    3. Zaicev M., “Residual Finiteness and Representability of Lie-Algebras”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1995, no. 3, 88–91  mathscinet  isi
    4. M. V. Zaitsev, “Finiteness conditions on special Lie algebras”, Journal of Mathematical Sciences (New York), 88:4 (1998), 537  crossref  mathscinet  zmath
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:242
    Full text:67
    References:46
    First page:3

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021