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

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.