Space-time dynamics from algebra representations

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