An extension of the principle of relativity for one-dimensional space

The class of accelerated reference frames has been studied, on the basis of Fermi-Walker coordinates; both in the cases of uniform and arbitrary accelerations. In the first case, explicit formulae for the transformation of coordinates have been derived and, in both cases, we have also obtained the infinitesimal generators and their commutation relations. The outcome has been an extension of the Poincar\'e algebra (in 1+1 dimensions), which is infinite dimensional in the case of general acceleration. This extension turns out to be trivial, in the sense that it is Abelian.