  A model for 2D-quantum gravity from the Virasoro symmetry is studied. The
notion of space-time naturally arises as a homogeneous space associated with
the kinematical (non-dynamical) SL(2,R) symmetry in the kernel of the
Lie-algebra central extension for the critical values of the conformal anomaly.
The rest of the generators in the group, L_n (n>1, n<-1), mix space-times with
different constant curvature. Only in the classical limit all space-times can
be identified, defining a unique Minkowski space-time, and the operators L_n
(n<1, n<-1) gauged away. This process entails a restriction to SL(2,R)
subrepresentations, which creates a non-trivial two-dimensional symplectic
classical phase space. The present model thus suggests that the role of general
covariance in quantum gravity is different from that played in the classical
limit.
