N=1 Supergravity and Maxwell superalgebras

We present the construction of the $D=4$ supergravity action from the minimal Maxwell superalgebra $s{\mathcal{M}}_4$, which can be derived from the $\mathfrak{o}\mathfrak{s}\mathfrak{p}\left(4\mathrm{\mid }1\right)$ superalgebra by applying the abelian semigroup expansion procedure. We show that $N=1$, $D=4$ pure supergravity can be obtained alternatively as the MacDowell-Mansouri like action built from the curvatures of the Maxwell superalgebra $s{\mathcal{M}}_4$. We extend this result to all minimal Maxwell superalgebras type $s{\mathcal{M}}_{m+2}$. The invariance under supersymmetry transformations is also analized.