Killing Symmetries of Generalized Minkowski Spaces, 3: Spacetime Translations in Four Dimensions

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a (in general non-diagonal) metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves (without loss of generality) to the four-dimensional case. In particular, the results obtained are specialized to the case of a deformed Minkowski space (i.e. a pseudoeuclidean space with metric coefficients depending on energy).