Computing an invariant of a closed star-product over a symplectic manifold (Q1809239)

\textit{A. Connes, M. Flato} and \textit{D. Sternheimer} [Lett. Math. Phys. 24, 1-12 (1992; Zbl 0767.55005)] constructed an invariant \(\phi \) in the cyclic homology of a symplectic manifold \(M\) for any closed star-product and computed this invariant in the de Rham complex for the case \(M=T^* V\). In the present paper, the author gives a generalization by computing the image of \(\phi \) in the de Rham complex for any symplectic manifold and any closed star-product. Also, this invariant is related to the work of \textit{M. Kontsevich} [Math. Phys. Stud. 20, 139-156 (1997; MR 98m:58044)] in which the existence of star-products on Poisson manifolds and a method of classification is proved.