Teoria delle rappresentazioni di gruppi e algebre di Lie in meccanica del corpo rigido

In this thesis it will be presented the basic facts about Lie groups and algebras representation theory, with particular attention to adjoint and co-adjoint representations. Later on it will be discussed the Lie-Poisson reduction theorem in rigid body mechanics, as well as the Hamiltonian formalism for the rigid body. It will be shown that the Lie-Poisson formalism can be expressed in terms of coadjoint representation, thus giving an example of the use of this type of representation.