The group of Abelian supersymmetry transformations isomorphic to groups of superspace tetrad transformations

Through a series of papers many results in group theory have been proven. These results establish a direct link between the local gauge groups of transformations of the Standard Model and local groups of transformations of a new kind of tetrad vectors in four-dimensional Lorentzian spacetimes. These links between these two sets of local groups of transformations are isomorphisms. Since the new groups allow for a geometrical reinterpretation of particle multiplets as multiplets associated to the invariance of a gravitational field, instead of mass multiplets, the stress-energy tensors and their associated local planes of diagonalization become relevant. Because the local planes of covariant diagonalization of stress-energy tensors in Yang-Mills theories have been proven to be the local planes of gauge symmetry, simultaneously. It is in this context that we wish to establish a new kind of relationship. We will explore the possible application of supersymmetry in superspace using four-dimensional Lorentzian tetrads. Since all internal local groups of transformations of the Standard Model have been proved to be isomorphic to local groups of tetrad transformations, we will study the internal local Abelian supersymmetry driving a local tetrad transformation. In the end the Abelian group of supersymmetry transformations will be proven to be isomorphic to Homothetic groups of superspace tetrad transformations.