Computing an invariant of a closed star-product over a symplectic manifold
type: Item
instance of: scholarly article
title: Computing an invariant of a closed star-product over a symplectic manifold
zbMATH Open document ID: 0939.53045
author: Gilles Halbout
published in: Communications in Mathematical Physics
publication date: 1999-12-16T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 53D55
zbMATH DE Number: 1379904
zbMATH Keywords: symplectic and Poisson manifold
zbMATH Keywords: star-product
zbMATH Keywords: Riemann-Roch type theorem
zbMATH Keywords: cyclic cohomology
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: s002200050666
OpenAlex ID: W2035968643
DOI: 10.1007/S002200050666
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description: scientific article; zbMATH DE number 1379904