Geometrical aspects of the Lie algebra S-expansion procedure

In this article it is shown that S-expansion procedure affects the geometry of a Lie group, changing it and leading us to the geometry of another Lie group with higher dimensionality. A method for determining the semigroup, which would provide a Lie algebra from another, is outlined via an example. Finally, it is proved that a Lie algebra obtained from another Lie algebra via S-expansion is a non-simple Lie algebra.