Hopf solitons and area-preserving diffeomorphisms of the sphere

We consider a (3+1)-dimensional local field theory defined on the sphere S- 2. The model possesses exact soliton solutions with nontrivial Hopf topolog ical charges and an infinite number of local conserved currents. We show th at the Poisson bracket algebra of the corresponding charges is isomorphic t o that of the area-preserving diffeomorphisms of the sphere S-2. We also sh ow that the conserved currents under consideration are the Noether currents associated to the invariance of the Lagrangian under that infinite group o f diffeomorphisms. We indicate possible generalizations of the model.