  The faithful representations of real Lie algebras g with dimensions $n\leq 4$
acting on the dual space of the universal covering algebra of an ideal s of g,
are calculated. With the help of left and right translations of the Lie group,
we define the homogeneous manifolds of dimension n and we calculate the Killing
fields (generators of left translations), the invariant fields (generators of
right translations) and the left invariant 1-forms.
