Abstract
We give a direct elementary proof of the existence of traces for arbitrary star products on a symplectic manifold. We follow the approach we used in [J. Geom. Phys. 29 (1999) 347], solving first the local problem. A normalisation introduced by Karabegov [Lett. Math. Phys. 45 (1998) 217] makes the local solutions unique and allows them to be pieced together to solve the global problem.
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