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

الأصل · EN

Let (g,δℏ) be a Lie bialgebra. Let (Uℏ(g),Δℏ) a quantization of (g,δℏ) through Etingof-Kazhdan functor. We prove the existence of a L∞-morphism between the Lie algebra C()=Λ(g) and the tensor algebra TU=T(Uℏ(g)[-1]) with Lie algebra structure given by the Gerstenhaber bracket. When (g,δℏ,r) is a coboundary Lie bialgebra, we deduce from the formality morphism the existence of a quantization R of r.