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

Abstract

Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. Also, we study Jacobi-Lie systems on these real low-dimensional Lie groups. Our results are illustrated through examples of Jacobi-Lie Hamiltonian systems on some real two- and three-dimensional Lie groups.

arXiv comment17pages

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• Contact Lie systems
• Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries
• Jacobi-Lie Models and Supergravity Equations
• Plane-parallel waves as Jacobi-Lie models
• Nonlinear Lie-Hamilton systems: $t$-Dependent curved oscillators and Kepler-Coulomb Hamiltonians
• Hamiltonian stochastic Lie systems and applications
• Integrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groups