On the inverse mapping of the formal symplectic groupoid of a deformation quantization

Details On the inverse mapping of the formal symplectic groupoid of a deformation quantization On the inverse mapping of the formal symplectic groupoid of a deformation quantization

2004-03-28

arxiv.org/abs/math/0403488v1

Mathematics

Quantum Algebra

14 pages, latex

Scientific paper

10.1007/s11005-004-0610-1

To each natural star product on a Poisson manifold $M$ we associate an antisymplectic involutive automorphism of the formal neighborhood of the zero section of the cotangent bundle of $M$. If $M$ is symplectic, this mapping is shown to be the inverse mapping of the formal symplectic groupoid of the star product. The construction of the inverse mapping involves modular automorphisms of the star product.

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