L-infinity Algebras of Gravity and their Braided Deformations

Abstract: In this talk we will describe the cyclic $L_\infty$-algebra formulation of classical general relativity without matter fields in the Einstein-Cartan (EC) formalism. We will start with a brief review of $L_\infty$-algebra and then apply this formalism to the EC gravity. After discussing the $L_\infty$ structure of classical (undeformed) gravity, we will present the $L_\infty$ formulation of noncommutative (deformed, braided) gravity. The noncommutativity is introduced via the Drinfeld twist and the corresponding symmetries (diffeomorphisms and local Lorentz symmetry) are given in terms of twisted (braided) Hopf-algebras. For simplicity, we will discuss only the three and four-dimensional cases. Nevertheless, the whole construction can be done in an arbitrary dimensional case.

Mathematics

Audience: researchers in the topic

Seminario de Geometría y Física - Matemática UCN-USP