An extension of Poincar\'e group abiding arbitrary acceleration

The class of accelerated reference frames has been studied, on the basis of Fermi-Walker coordinates. The infinitesimal transformations connecting two of these frames has been obtained, and also their commutation relations. The outcome is an infinite dimensional extension of the Poincar\'e algebra. Although this extension turns out to be Abelian, and hence trivial, it is noteworthy that, contrarily to what happens with Lorentz boosts, acceleration boost generators commute with each other and with translation generators.