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Mat. Sb., 2014, Volume 205, Number 1, Pages 47–66 (Mi msb8197)  

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

Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation

A. Yu. Konyaev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We provide a complete list of real Lie algebras with generic orbits of dimension 2 in the coadjoint representation.
Bibliography: 20 titles.

Keywords: Poisson bracket, Lie algebra, coadjoint representation, integrable systems.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-1410.2012.1
14.740.11.0794
14.740.11.0876
11.G34.31.0054


DOI: https://doi.org/10.4213/sm8197

Full text: PDF file (550 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:1, 45–62

Bibliographic databases:

UDC: 514.747.2
MSC: Primary 17B08; Secondary 17B80, 53D17
Received: 10.12.2012 and 15.10.2013

Citation: A. Yu. Konyaev, “Classification of Lie algebras with generic orbits of dimension 2 in the coadjoint representation”, Mat. Sb., 205:1 (2014), 47–66; Sb. Math., 205:1 (2014), 45–62

Citation in format AMSBIB
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    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. Fomenko A.T., Konyaev A.Yu., “Geometry, Dynamics and Different Types of Orbits”, J. Fixed Point Theory Appl., 15:1 (2014), 49–66  crossref  mathscinet  zmath  isi  elib  scopus
    2. I. A. Bizyaev, A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Topology and bifurcations in nonholonomic mechanics”, International Journal of Bifurcation and Chaos, 25:10 (2015), 15300–21  mathnet  crossref  isi
    3. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Hojman Construction and Hamiltonization of Nonholonomic Systems”, SIGMA, 12 (2016), 012, 19 pp.  mathnet  crossref
    4. Shapovalov A.V., Trifonov A.Yu., “Approximate Solutions and Symmetry of a Two-Component Nonlocal Reaction-Diffusion Population Model of the Fisher-Kpp Type”, Symmetry-Basel, 11:3 (2019), 366  crossref  zmath  isi
    5. Alexey Bolsinov, Jinrong Bao, “A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras”, Regul. Chaotic Dyn., 24:3 (2019), 266–280  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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