Universal star products

英文摘要：

One defines the notion of universal deformation quantization: given any manifold $M$, any Poisson structure $¶$ on $M$ and any torsionfree linear connection $\nabla$ 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.