Universal Star Products |
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Authors: | Mourad Ammar Véronique Chloup Simone Gutt |
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Affiliation: | 1. Université du Luxembourg, avenue de la fa?encerie, Luxembourg, Luxembourg 2. Université Paul Verlaine - Metz, LMAM Ile du Saulcy, 57045, Metz Cedex 01, France 3. Université Libre de Bruxelles, Campus Plaine CP 218, Bvd du Triomphe, 1050, Brussels, Belgium
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Abstract: | One defines the notion of universal deformation quantization: given any manifold M, any Poisson structure Λ on M and any torsionfree linear connection ? on M, a universal deformation quantization associates to this data a star product on (M, Λ) given by a series of bidifferential operators whose corresponding tensors are given by universal polynomial expressions in the Poisson tensor Λ, the curvature tensor R and their covariant iterated derivatives. Such universal deformation quantization exist. We study their unicity at order 3 in the deformation parameter, computing the appropriate universal Poissoncohomology. |
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