On free Lie algebras and particles in electro-magnetic fields

The Poincaré algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electromagnetic backgrounds and possibly including the backreaction due the presence of multipoles. We point out a relation of this construction to free Lie algebras that gives a unified description of all possible kinematic extensions, leading to a symmetry algebra that we call Maxwell∞. A specific dynamical system with this infinite symmetry is constructed and analysed.SCOPUS: ar.j