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arXiv · 0804.1300

Universal star products

Mourad Ammar·Veronique Chloup·Simone Gutt
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Abstract

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.

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Mourad Ammar, Veronique Chloup, Simone Gutt. 2008-04-08. Universal star products. https://doi.org/10.1007/s11005-008-0240-0

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