Generalized relativistic kinematics

We propose a method for deforming an extended Galilei algebra that leads to a nonstandard realization of the Poincaré group with the Fock–Lorentz linear fractional transformations. The invariant parameter in these transformations has the dimension of length. Combining this deformation with the standard one (with an invariant velocity $c$) leads to the algebra of the symmetry group of the anti-de Sitter space in Beltrami coordinates. In this case, the action for free point particles contains the dimensional constants $R$ and $c$. The limit transitions lead to the ordinary ($R\to\infty$) or alternative ($c\to\infty$) but nevertheless relativistic kinematics.