Equivalence of star products on a symplectic manifold; an introduction to Deligne’s Čech cohomology classes. (English) Zbl 1024.53057

Gutt, Simone; Rawnsley, John

J. Geom. Phys. 29, No. 4, 347-392 (1999).

Summary: These notes grew out of the Quantisation Seminar 1997-1998 on Deligne’s paper [P. Deligne, Sel. Math., New Ser. 1, 667-697 (1995; Zbl 0852.58033)] and the lecture of the first author in the Workshop on Quantisation and Momentum Maps at the University of Warwick in December 1997. We recall the definitions of the cohomology classes introduced by Deligne for equivalence classes of differential star products on a symplectic manifold and show the properties of and relations between these classes by elementary methods based on Čech cohomology.

MSC:

53D55	Deformation quantization, star products
53D05	Symplectic manifolds (general theory)
58H15	Deformations of general structures on manifolds

Keywords:

differential star products; symplectic manifold; Čech cohomology

Citations:

Zbl 0852.58033

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