Equivalence of star products on a symplectic manifold; an introduction to Deligne's Čech cohomology classes

Abstract

These notes grew out of the Quantisation Seminar 1997–1998 on Deligne's paper [P. Deligne, Déformations de l'algèbre des fonctions d'une variété symplectique: Comparison entre Fedosov et De Wilde, Lecomte, Selecta Math. (New Series) 1 (1995) 667–697] and the lecture of the first author in the Workshop on Quantisation and Momentum Maps at the University of Warwich in December 1997. We recall the definitions of the cohomology classes introduced by Deligne for equivalence classes of differential star products on a symplectic manfold and show the properties of the relations between these classes by elementary methods based on Čech cohomology.