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

## TL;DR

This paper extends the Poincaré group by incorporating generalized Fermi-Walker coordinates, revealing an infinite-dimensional Abelian extension where acceleration and rotation generators commute with Poincaré generators.

## Contribution

It introduces an infinite-dimensional extension of the Poincaré algebra based on generalized Fermi-Walker coordinates, highlighting unique commutation properties.

## Key findings

- Infinite-dimensional Abelian extension of Poincaré algebra
- Acceleration and rotational generators commute with Poincaré generators
- Explicit infinitesimal transformations between accelerated frames

## Abstract

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.