Formality theorem for Lie bialgebras and quantization of twists and coboundary r-matrices |
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Authors: | Gilles Halbout |
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Institution: | IRMA (CNRS), rue René Descartes, F-67084 Strasbourg, France |
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Abstract: | Let (g,δ?) be a Lie bialgebra. Let (U?(g),Δ?) a quantization of (g,δ?) through Etingof-Kazhdan functor. We prove the existence of a L∞-morphism between the Lie algebra C(g)=Λ(g) and the tensor algebra (without unit) T+U=T+(U?(g)−1]) with Lie algebra structure given by the Gerstenhaber bracket. When s is a twist for (g,δ), we deduce from the formality morphism the existence of a quantum twist F. When (g,δ,r) is a coboundary Lie bialgebra, we get the existence of a quantization R of r. |
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Keywords: | Lie algebras Quantization Morphisms up to homotopy Twists |
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