Space-time dynamics from algebra representations

We present a model for introducing dynamics into a space-time geometry. This space-time structure is constructed from a C*-algebra defined in terms of the generators of an irreducible unitary representation of a finite-dimensional Lie algebra G. This algebra is included as a subalgebra in a bigger algebra F, the generators of which mix the representations of G in a way that relates different space-times and creates the dynamics. This construction can be considered eventually as a model for two-dimensional quantum gravity.