An abelian approach to symplectic reduction for a certain class of groups and momentum values.

The thesis concerns the formulation of a particular instance of symplectic reduction by stages in which the symmetry group M has the normal part N which is abelian. In this setting, if one reduces with respect to precise momentum values, the second reduction happens to be trivial, so that the full reduced space is symplectomorphic to the first stage reduction space. This framework fits the case where the ambient group has a semidirect structure of a group G acting on a vector space V. Applying the theorem here we recover a consequence on the grometry of coadjoint orbits through "non generic" values in $\mathfrak{m}^*$. The thesis also shows several examples on which the result applies (or not).