Non-relativistic four dimensional p-brane supersymmetric theories and Lie algebra expansion

We apply the Lie algebra expansion method to the N = 1 super-Poincare algerba in four dimensions. We define a set of p-brane projectors that induce a decomposition of the super-Poincare algebra preparatory for the expansion. We show that starting from the N = 1 supergravity action in four dimensions it is possible to obtain non-relativistic supersymmetric theories, describing strings or membranes.