An extension of Poincar\'e group based on generalized Fermi-Walker coordinates

The class of accelerated and rotating reference frames has been studied on the basis of generalized Fermi-Walker coordinates. We obtain the infinitesimal transformations connecting any two of these frames and also their commutation relations. We thus have an infinite dimensional extension of the Poincar\'e algebra and, although it turns out to be Abelian extension, and hence trivial, it is noteworthy that, contrarily to Lorentz boosts, acceleration and rotational boost generators commute with each other and with the generators of Poincar\'e group as well.