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.