  An object is chiral when its symmetry group contains no indirect isometry. It
can be difficult to classify isometries as direct or indirect, except in the
Euclidean case. We classify them with the help of outer semidirect products of
isometry groups, in particular in the case of an affine space defined over a
finite-dimensional real quadratic space. We also classify as direct or indirect
the isometries of the real Lorentz-Minkowski spacetime and those of the
classical spacetime defined by the Newton-Cartan theory.
