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

These notes grew out of the Quantisation Seminar 1997-1998 on Deligne's paper [P. Deligne, Deformations de l'algebre des fonctions d'une variete symplectique: Comparaison 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 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 Cech cohomology. (C) 1999 Elsevier Science B.V. All rights reserved. Subj. Class.: Differential geometry; Quantum mechanics 1991 MSG: 53015; 58705.