N=1 supergravity and Maxwell superalgebras

We present the construction of the D = 4 supergravity action from the minimal Maxwell superalgebra sℳ4, which can be derived from the osp4|1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{osp}\ \left(4\Big|1\right) $$\end{document} 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 sℳ4. We extend this result to all minimal Maxwell superalgebras type sℳm + 2. The invariance under supersymmetry transformations is also analized.