Homotopy lie algebras of gravity and their braided deformations

Abstract

We describe the cyclic L∞-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∞-algebra, and use it to encode the symmetries, field content, field equations and Noether identities of noncommutative gravity.