RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
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



TMF:
Year:
Volume:
Issue:
Page:
Find






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


TMF, 2000, Volume 123, Number 2, Pages 345–352 (Mi tmf608)  

This article is cited in 3 scientific papers (total in 4 papers)

Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable

A. M. Vershika, B. B. Shoikhetb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Independent University of Moscow

Abstract: We define a class of infinite-dimensional Lie algebras that generalize the universal enveloping algebra of the algebra $sl(2,\mathbb C)$ regarded as a Lie algebra. These algebras are a special case of $\mathbb Z$-graded Lie algebras with a continuous root system, namely, their Cartan subalgebra is the algebra of polynomials in one variable. The continuous limit of these algebras defines new Poisson brackets on algebraic surfaces.

DOI: https://doi.org/10.4213/tmf608

Full text: PDF file (222 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2000, 123:2, 701–707

Bibliographic databases:


Citation: A. M. Vershik, B. B. Shoikhet, “Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable”, TMF, 123:2 (2000), 345–352; Theoret. and Math. Phys., 123:2 (2000), 701–707

Citation in format AMSBIB
\Bibitem{VerSho00}
\by A.~M.~Vershik, B.~B.~Shoikhet
\paper Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable
\jour TMF
\yr 2000
\vol 123
\issue 2
\pages 345--352
\mathnet{http://mi.mathnet.ru/tmf608}
\crossref{https://doi.org/10.4213/tmf608}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794166}
\zmath{https://zbmath.org/?q=an:1017.17029}
\elib{http://elibrary.ru/item.asp?id=13347389}
\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 123
\issue 2
\pages 701--707
\crossref{https://doi.org/10.1007/BF02551403}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000165897000014}


Linking options:
  • http://mi.mathnet.ru/eng/tmf608
  • https://doi.org/10.4213/tmf608
  • http://mi.mathnet.ru/eng/tmf/v123/i2/p345

    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. Vershik, AM, “Graded Lie algebras and dynamical systems”, Acta Applicandae Mathematicae, 73:1–2 (2002), 239  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. Zuevsky, A, “Noncommutative (*)-product continual Lie algebras and solvable models”, Czechoslovak Journal of Physics, 54:5 (2004), 501  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    3. Zuevsky, A, “Continual Lie algebras and noncommutative counterparts of exactly solvable models”, Journal of Physics A-Mathematical and General, 37:2 (2004), 537  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:362
    Full text:125
    References:42
    First page:6

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020