  We define an Isometry germ at any given event $x$ of space-time as a vector
field $\xi$ defined in a neighborhood of $x$ such that the Lie derivative of
both the metric and the Riemannian connection are zero at this event. Two
isometry germs can be said to be equivalent if their values and the values of
their first derivatives coincide at $x$. The corresponding quotient space can
be endowed with a structure of a bracket algebra which is a deformation of de
Sitter's Lie algebra. Each isometry germ defines also a local stationary frame
of reference, the consideration of the family of adapted coordinate
transformations between any two of them leading to a local novel structure that
generalizes the Lorentz group.
