  The expansion of a Lie algebra entails finding a new, bigger algebra G,
through a series of well-defined steps, from an original Lie algebra g. One
incarnation of the method, the so-called S-expansion, involves the use of a
finite abelian semigroup S to accomplish this task. In this paper we put
forward a dual formulation of the S-expansion method which is based on the dual
picture of a Lie algebra given by the Maurer-Cartan forms. The dual version of
the method is useful in finding a generalization to the case of a gauge free
differential algebra, which in turn is relevant for physical applications in,
e.g., Supergravity. It also sheds new light on the puzzling relation between
two Chern-Simons Lagrangians for gravity in 2+1 dimensions, namely the
Einstein-Hilbert Lagrangian and the one for the so-called "exotic gravity".
