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Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson–Lie groups

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Abstract

We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical r-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson–Lie groups. We obtain some new integrable models where a Poisson–Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system.

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Authors and Affiliations

  1. Department of Mathematics, University of Bonab, Tabriz, Iran

    J. Abedi-Fardad & Gh. Haghighatdoost

  2. Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran

    J. Abedi-Fardad & A. Rezaei-Aghdam

  3. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Gh. Haghighatdoost

Authors
  1. J. Abedi-Fardad
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  2. A. Rezaei-Aghdam
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  3. Gh. Haghighatdoost
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Corresponding author

Correspondence to J. Abedi-Fardad.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 1, pp. 3–20, January, 2017.

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Abedi-Fardad, J., Rezaei-Aghdam, A. & Haghighatdoost, G. Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson–Lie groups. Theor Math Phys 190, 1–17 (2017). https://doi.org/10.1134/S0040577917010019

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  • DOI: https://doi.org/10.1134/S0040577917010019

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