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.
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
\Bibitem{AmiHagKhe20}
\by H.~Amirzadeh-Fard, Gh.~Haghighatdoost, P.~Kheradmandynia, A.~Rezaei-Aghdam
\paper Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi--Lie systems
\jour TMF
\yr 2020
\vol 205
\issue 2
\pages 171--189
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\transl
\jour Theoret. and Math. Phys.
\yr 2020
\vol 205
\issue 2
\pages 1393--1410
\crossref{https://doi.org/10.1134/S004057792011001X}
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Linking options:
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:
Ivo Petr, Ladislav Hlavatý, “Plane-parallel waves as Jacobi–Lie models”, Class. Quantum Grav., 42:5 (2025), 055007
Ladislav Hlavatý, Ivo Petr, “Jacobi–Lie Models and Supergravity Equations”, Progress of Theoretical and Experimental Physics, 2024:5 (2024)
J. de Lucas, X. Rivas, “Contact Lie systems: theory and applications”, J. Phys. A: Math. Theor., 56:33 (2023), 335203
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
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