Lie algebras connected with infinite momentum kinematics

In this paper we investigate the Lie algebras obtained from the infinite momentum limit of the Poincaré group. It will be shown that this limit depends upon a real, nonnegative number γ, and so do the structure constants of the resulting Lie algebra, which has three singular points γ = 1,0,∞. The last two singularities give algebras isomorphic to two different contractions of the algebra of the Poincaré group, while the case γ = 1 gives an algebra which cannot be obtained in this fashion. Suggestions are provided towards a physical interpretation of these results.