Homotopy Lie Algebras of Gravity and their Braided Deformations

Abstract

We describe the cyclic $L_{\infty }$-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 $L_{\infty }$-algebra, and use it to encode the symmetries, field content, field equations and Noether identities of noncommutative gravity.

arXiv comment17 pages; Contribution to the Proceedings of the Workshop "Quantum Geometry, Field Theory and Gravity", Corfu Summer Institute on Elementary Particle Physics and Gravity, 31 August-25 September 2019, Corfu, Greece

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Cited by in corpus (3)

• Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry
• Braided Symmetries in Noncommutative Field Theory
• $L_{\infty }$-Algebras of Einstein-Cartan-Palatini Gravity