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.

17 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

References in corpus (4)

• A Gravity Theory on Noncommutative Spaces
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• Braided quantum field theories and their symmetries
• The graded Lie algebra of general relativity