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arXiv · 2507.20344

The $L_\infty$ structure of Free Differential Algebras and $d=11$ Supergravity

L. Castellani·R. D'Auria
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Abstract

We discuss free differential algebras (FDA's), a generalization of the Cartan-Maurer equations for the group manifold vielbein, appropriate for theories containing $p$-forms ($p >1$). Their dual formulation is an extension of Lie algebras, called $L_\infty$ algebras, and we illustrate this duality in a simple example. Finally we review the FDA structure and the dual $L_\infty$ structure of $d=11$ supergravity.

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L. Castellani, R. D'Auria. 2025-07-27. The $L_\infty$ structure of Free Differential Algebras and $d=11$ Supergravity. https://arxiv.org/abs/2507.20344

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