  The sO(3) and the Lorentz algebra symmetries breaking with gauge curvatures
are studied by means of a covariant Hamiltonian. The restoration of these
algebra symmetries in flat and curved spaces is performed and led to the
apparition of a monopole field. Then in the context of the Lorentz algebra we
consider an application to the gravitoelectromagnetism theory. In this last
case a qualitative relation giving a mass spectrum for dyons is established.
