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

• Autores: Gilles Halbout
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 2, 2006, págs. 617-633
• Idioma: inglés
• DOI: 10.1016/j.aim.2005.12.006
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• Resumen

  • 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.