2008/04/08 by Mourad Ammar, Veronique Chloup, Véronique Chloup +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.SG #msc:53D55 #msc:81S10
paper · pdf · doi:10.1007/s11005-008-0240-0
To appear in Letters in Mathematical Physics
arxiv created 2008/04/08 · openalex publication_date 2008/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One defines the notion of universal deformation quantization: given any manifold M, any Poisson structure ¶ on M and any torsionfree linear connection ∇ on M, a universal deformation quantization associates to this data a star product on (M,¶) given by a series of bidifferential operators whose corresponding tensors are given by universal polynomial expressions in the Poisson tensor ¶, 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 Poisson cohomology.