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

2005/06/23 by Gilles Halbout, Halbout, Gilles
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0506487

arxiv created 2005/06/23 · openalex publication_date 2005/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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