Kinematics of the Internal Space Associated with the TEGR

In the context of the teleparallel equivalent of general relativity - TEGR - we have obtained, through the second kind of gauge transformations, the most fundamental transformations, namely, the ones of the first kind. We show that considering the possibility of decomposing the components of the tetrad field as having a trivial part plus some potential besides the usual translational and Lorentz potentials, there is also the possibility that the symmetry group of the internal space can be a generalization of the Poincare group. Furthermore, in the analysis of the transformations in the internal space, we saw that for the case in which the decomposition of the tetrad field components include only a trivial part plus a translational potential, we are able to recover just the translational group. Moreover, the internal space of gravity must be the physical space - on a local scale - in such a way that the gauge symmetry group is the kinematical group of the physical space itself. This group was obtained, and seems to generalize the Poincare group.