In the present work we studied some Lie algebras. We can choose a Lie algebra L over the field R, when we use matrix representations for the elements in the base, we can use it to construct vector fields over a manifold M with the same commutation relations for the elements in the base, we find one parameter groups and we studied if the vector fields can be Killing vectors.
We use matrix representations to construct models with the first class constraints in a gauge system, we found complete observables and we obtained the Lie algebra of observables, too. We illustrate the methods with gl(2), sp(2, R), sl(3) and so on.
I would like to dedícate the present book to Ammie, Jean, their mother and my family.