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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 190, Number 1, Pages 3–20
DOI: https://doi.org/10.4213/tmf9020 (Mi tmf9020) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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

J. Abedi-Fardadab, A. Rezaei-Aghdama, Gh. Haghighatdoostcb

a Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran
b Department of Mathematics, University of Bonab, Tabriz, Iran
c Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Full-text PDF (557 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf9020
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.
Keywords: Lie bialgebra, Poisson–Lie group, classical r-matrix, integrable system.
Received: 04.08.2015
Revised: 21.12.2015
English version:
Theoretical and Mathematical Physics, 2017, Volume 190, Issue 1, Pages 1–17
DOI: https://doi.org/10.1134/S0040577917010019
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost, “Classification of four-dimensional real Lie bialgebras of symplectic type and their Poisson–Lie groups”, TMF, 190:1 (2017), 3–20; Theoret. and Math. Phys., 190:1 (2017), 1–17
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9020
  • https://doi.org/10.4213/tmf9020
  • https://www.mathnet.ru/eng/tmf/v190/i1/p3
    • This publication is cited in the following 6 articles:
    1. J. de Lucas, D. Wysocki, “Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras”, Symmetry-Basel, 13:3 (2021), 465  crossref  mathscinet  isi
    2. G. Haghighatdoost, S. Abdolhadi-Zangakani, J. Abedi-Fardad, “Compatible Poisson structures and bi-Hamiltonian systems related to low-dimensional Lie algebras”, J. Nonlinear Math. Phys., 28:2 (2021), 194–204  crossref  mathscinet  isi
    3. J. de Lucas, D. Wysocki, “A grassmann and graded approach to coboundary lie bialgebras, their classification, and Yang-Baxter equations”, J. Lie Theory, 30:4 (2020), 1161–1194  mathscinet  isi
    4. G. Haghighatdoost, Z. Ravanpak, A. Rezaei-Aghdam, “Some remarks on invariant Poisson quasi-Nijenhuis structures on lie groups”, Int. J. Geom. Methods Mod. Phys., 16:7 (2019), 1950097  crossref  mathscinet  isi  scopus
    5. Z. Ravanpak, A. Rezaei-Aghdam, G. Haghighatdoost, “Invariant Poisson–Nijenhuis structures on Lie groups and classification”, Int. J. Geom. Methods Mod. Phys., 15:4 (2018), 1850059  crossref  mathscinet  zmath  isi  scopus
    6. Abedi-Fardad J., Rezaei-Aghdam A., Haghighatdoost G., “Some Compatible Poisson Structures and Integrable Bi-Hamiltonian Systems on Four Dimensional and Nilpotent Six Dimensional Symplectic Real Lie Groups”, J. Nonlinear Math. Phys., 24:2 (2017), 149–170  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:488
    Full-text PDF :164
    References:65
    First page:22
     
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