Homotopy Lie Algebras of Gravity and their Braided Deformations

We describe the cyclic $L_{\mathrm{\infty }}$-algebra formulation of classical general relativity without matter fields in the Einstein-Cartan-Palatini formalism. Using Drinfel’d twist deformation techniques, we define a noncommutative version of the theory with braided gauge symmetries. We introduce a notion of braided $L_{\mathrm{\infty }}$-algebra, and use it to encode the symmetries, field content, field equations and Noether identities of noncommutative gravity.