On the Hidden Maxwell Superalgebra underlying D=4 Supergravity

Understand

In this work, we expand the hidden $AdS$-Lorentz superalgebra underlying $D=4$ supergravity, reaching a (hidden) Maxwell superalgebra.

• The latter can be viewed as an extension involving cosmological constant of the superalgebra underlying $D=4$ supergravity in flat spacetime.
• We write the Maurer-Cartan equations in this context and we find some interesting extensions of the antisymmetric $3$-form $A^{(3)}$ appearing in the Free Differential Algebra in Minkowski space.
• The structure of Free Differential Algebras is obtained by considering the zero curvature equations.