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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 2, Pages 171–189
DOI: https://doi.org/10.4213/tmf9927 (Mi tmf9927) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi–Lie systems

H. Amirzadeh-Farda, Gh. Haghighatdoosta, P. Kheradmandyniab, A. Rezaei-Aghdamb

a Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
b Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran
Full-text PDF (590 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf9927
Abstract: Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. We also study Jacobi–Lie systems on these real low-dimensional Lie groups and illustrate our results with examples of Jacobi–Lie Hamiltonian systems on some real two- and three-dimensional Lie groups.
Keywords: Lie group, Jacobi structure, Lie system, Jacobi–Lie system.
Received: 29.04.2020
Revised: 16.06.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 2, Pages 1393–1410
DOI: https://doi.org/10.1134/S004057792011001X
Bibliographic databases:
Document Type: Article
MSC: 70Hxx; 37Jxx
Language: Russian
Citation: H. Amirzadeh-Fard, Gh. Haghighatdoost, P. Kheradmandynia, A. Rezaei-Aghdam, “Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi–Lie systems”, TMF, 205:2 (2020), 171–189; Theoret. and Math. Phys., 205:2 (2020), 1393–1410
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9927
  • https://doi.org/10.4213/tmf9927
  • https://www.mathnet.ru/eng/tmf/v205/i2/p171
    • This publication is cited in the following 5 articles:
    1. Ivo Petr, Ladislav Hlavatý, “Plane-parallel waves as Jacobi–Lie models”, Class. Quantum Grav., 42:5 (2025), 055007  crossref
    2. Ladislav Hlavatý, Ivo Petr, “Jacobi–Lie Models and Supergravity Equations”, Progress of Theoretical and Experimental Physics, 2024:5 (2024)  crossref
    3. J. de Lucas, X. Rivas, “Contact Lie systems: theory and applications”, J. Phys. A: Math. Theor., 56:33 (2023), 335203  crossref  mathscinet
    4. H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam, “Integrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groups”, J. Nonlinear Math. Phys., 30:4 (2023), 1483  crossref  mathscinet
    5. H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam, “Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries”, J. Math. Phys. Anal. Geom., 18:1 (2022), 33  crossref  mathscinet
    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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