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SIGMA, 2014, Volume 10, 056, 18 pp. (Mi sigma921)  

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

Integrable Systems Related to Deformed $\mathfrak{so}(5)$

Alina Dobrogowska, Anatol Odzijewicz

Institute of Mathematics, University of Białystok, Lipowa 41, 15-424 Białystok, Poland

Abstract: We investigate a family of integrable Hamiltonian systems on Lie–Poisson spaces $\mathcal{L}_+(5)$ dual to Lie algebras $\mathfrak{so}_{\lambda, \alpha}(5)$ being two-parameter deformations of $\mathfrak{so}(5)$. We integrate corresponding Hamiltonian equations on $\mathcal{L}_+(5)$ and $T^*\mathbb{R}^5$ by quadratures as well as discuss their possible physical interpretation.

Keywords: integrable Hamiltonian systems; Casimir functions; Lie algebra deformation; symplectic dual pair; momentum map.

DOI: https://doi.org/10.3842/SIGMA.2014.056

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Full text: http://www.emis.de/journals/SIGMA/2014/056/
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Bibliographic databases:

ArXiv: 1311.0679
MSC: 70H06; 37J15; 53D17
Received: November 5, 2013; in final form May 26, 2014; Published online June 3, 2014
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Citation: Alina Dobrogowska, Anatol Odzijewicz, “Integrable Systems Related to Deformed $\mathfrak{so}(5)$”, SIGMA, 10 (2014), 056, 18 pp.

Citation in format AMSBIB
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\by Alina~Dobrogowska, Anatol~Odzijewicz
\paper Integrable Systems Related to Deformed $\mathfrak{so}(5)$
\jour SIGMA
\yr 2014
\vol 10
\papernumber 056
\totalpages 18
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\crossref{https://doi.org/10.3842/SIGMA.2014.056}
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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. Dobrogowska A., Golinski T., “Lie Bundle on the Space of Deformed Skew-Symmetric Matrices”, J. Math. Phys., 55:11 (2014), 113504  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Dobrogowska A., Jakimowicz G., “Symplectic Dual Pair Related To So(a1,) (...) (,) (An-1) (N)”, Xxii International Conference on Integrable Systems and Quantum Symmetries (Isqs-22), Journal of Physics Conference Series, 563, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2014, 012009  crossref  isi  scopus
    3. Dobrogowska A., “R-Matrix, Lax pair, and Multiparameter Decompositions of Lie Algebras”, J. Math. Phys., 56:11 (2015), 113508  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Dobrogowska, A.; Golinski, T., “Examples of Hamiltonian systems on the space of deformed skew-symmetric matrices”, Trends in Mathematics, 71 (2015), 247-255  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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