Resumen de Formality theorem for Lie bialgebras and quantization of twists and coboundary r-matrices

Gilles Halbout

• Let be a Lie bialgebra. Let a quantization of through Etingof¿Kazhdan functor. We prove the existence of a L8-morphism between the Lie algebra and the tensor algebra (without unit) with Lie algebra structure given by the Gerstenhaber bracket. When s is a twist for , we deduce from the formality morphism the existence of a quantum twist F. When is a coboundary Lie bialgebra, we get the existence of a quantization R of r.