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Algebra i Analiz, 1992, Volume 4, Issue 6, Pages 103–113 (Mi aa358)  
This article is cited in 3 scientific papers (total in 4 papers)

Research Papers

Lie algebras generated by dynamical systems

A. M. Vershik

Saint-Petersburg State University
Full-text PDF (542 kB) Citations (4)
Abstract: In this paper we define the class of infinite dimensional $\mathbb Z$-graded Lie algebras generated by dynamical systems and show that these algebras are the special case of .Lie algebras with continuum root system. We establish a precise isomorphism between “sinealgebras” and “rotation-Lie-algebras”, and give the other examples. We briefly mention the algebras of the type $(B)(D)$ and $(C)$ for the dynamical system.
Keywords: Lie algebra, root system, dynamic system, rotation algebra, continuous Dyrikin diagram, $B-C-D$-series.
Received: 05.07.1992
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. M. Vershik, “Lie algebras generated by dynamical systems”, Algebra i Analiz, 4:6 (1992), 103–113; St. Petersburg Math. J., 4:6 (1993), 1143–1151
Citation in format AMSBIB
\Bibitem{Ver92}
\by A.~M.~Vershik
\paper Lie algebras generated by dynamical systems
\jour Algebra i Analiz
\yr 1992
\vol 4
\issue 6
\pages 103--113
\mathnet{http://mi.mathnet.ru/aa358}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1199636}
\zmath{https://zbmath.org/?q=an:0848.17036}
\transl
\jour St. Petersburg Math. J.
\yr 1993
\vol 4
\issue 6
\pages 1143--1151
Linking options:
  • https://www.mathnet.ru/eng/aa358
  • https://www.mathnet.ru/eng/aa/v4/i6/p103
    • This publication is cited in the following 4 articles:
    1. Andrea Appel, Francesco Sala, Olivier Schiffmann, “Continuum Kac–Moody algebras”, Mosc. Math. J., 22:2 (2022), 177–224  mathnet
    2. Vershik, AM, “Graded Lie algebras and dynamical systems”, Acta Applicandae Mathematicae, 73:1–2 (2002), 239  crossref  mathscinet  zmath  isi
    3. A. M. Vershik, B. B. Shoikhet, “Graded Lie algebras whose Cartan subalgebra is the algebra of polynomials in one variable”, Theoret. and Math. Phys., 123:2 (2000), 701–707  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. I. Arnol'd, M. Sh. Birman, I. M. Gel'fand, I. A. Ibragimov, S. V. Kerov, A. A. Kirillov, O. A. Ladyzhenskaya, G. A. Leonov, A. A. Lodkin, S. P. Novikov, Ya. G. Sinai, M. Z. Solomyak, L. D. Faddeev, “Anatolii Moiseevich Vershik (on his sixtieth birthday)”, Russian Math. Surveys, 49:3 (1994), 207–221  mathnet  crossref  mathscinet  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:480
    Full-text PDF :310
    References:2
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