  We review the geometrical formulation of Quantum Mechanics to identify,
according to Klein's programme, the corresponding group of transformations. For
closed systems, it is the unitary group. For open quantum systems, the
semigroup of Kraus maps contains, as a maximal subgroup, the general linear
group. The same group emerges as the exponentiation of the $C^{*}$--algebra
associated with the quantum system, when thought of as a Lie algebra. Thus,
open quantum systems seem to identify the general linear group as associated
with quantum mechanics and moreover suggest to extend the Klein programme also
to groupoids. The usual unitary group emerges as a maximal compact subgroup of
the general linear group.
