Cariche centrali nelle teorie di supergravità dimensionalmente ridotte e legame con la struttura algebrica L-infinity della gerarchia tensoriale.

When trying to relate theories in D+n dimensions with theories in D dimensions by means of a dimensional reduction, new generators emerge in the lower dimensional theory. These generators are non-writable as a combination of the isometries of the scalar manifold of the initial theory and commute with them, therefore these new generators are central charges in the dimensional reduced theory. The mathematical formulation used to used to deal with these aspects of supergravity theories the one that requires the use of the embedding tensor, useful for expressing gauge generators as a function of the isometries of the scalar manifold. The main reason why it is introduced this formalism is that it allows to pass from a gauge theory in the electric frame to a generic symplectic frame at the price of adding new dual magnetic fields and new constraints so as not to vary the total number of degrees of freedom of the theory. The consequence of adding magnetic dual fields is the loss of invariance with respect to gauge transformations of the symmetry group of the Lagrangian. In addition, the Jacobi identity for the structure constant that appears in the field strength is no longer valid and this leads to a violation of the Bianchi identity for the field strength. By appropriately redefining the fields of the theory by introducing new tensors it is possible to restore the gauge invariance. The new fields, that must be taken into consideration to do that, can be grouped according to a L∞ algebra structure in which each graded subspace can be decomposed into a part containing only the truly physical components of the theory that satiefies the Bianchi identity and a part containing the components that lead to the violation of the Bianchi identity. By using an appropriate basis it is therefore possible to decompose any object of the theory into these two components, and in particular, working with gauge generators, these are decomposed into generators that can be written as a combination of the isometries of the symmetry group and central charges. In this work, The tensor hierarchy will be analyzed and the central charges will be characterized in detail. Then these conceps will be applied to the maximal 4-dimensional supergravity theory obtained by means of a dimensional reduction of th 11-dimensional theory on a 7-torus T 7.