  Minkowski spacetime is transitive under ordinary translations, a
transformation that do not have matrix representations. The de Sitter
spacetime, on the other hand, is transitive under a combination of translations
and proper conformal transformations, which do have a matrix representation.
Such matrix, however, is not by itself a de Sitter generator: it gives rise to
a conformal re-scaling of the metric, a transformation not belonging to the de
Sitter group, and in general not associated with diffeomorphisms in spacetime.
When dealing with variational principles and Noether's theorem in de Sitter
spacetime, therefore, it turns out necessary to regularise the transformations
in order to eliminate the conformal re-scaling of the metric.
