  It is well known that velocities does not commute in presence of an
electromagnetic field. This property implies that angular algebra symmetries,
such as the sO(3) and Lorentz algebra symmetries, are broken. To restore these
angular symmetries we show the necessity of adding the Poincare momentum M to
the simple angular momentum L. These restorations performed succesively in a
flat space and in a curved space lead in each cases to the generation of a
Dirac magnetic monopole. In the particular case of the Lorentz algebra we
consider an application of our theory to the gravitoelectromagnetism. In this
last case we establish a qualitative relation giving the mass spectrum for
dyons.
