The L∞ structure of free differential algebras and d=11 supergravity

We discuss free differential algebras (FDAs), a generalization of the Cartan–Maurer equations for the group manifold vielbein, appropriate for theories containing p-forms ([Formula: see text]). Their dual formulation is an extension of Lie algebras, called [Formula: see text] algebras, and we illustrate this duality in a simple example. Finally, we review the FDA structure and the dual [Formula: see text] structure of [Formula: see text] supergravity.