Deformations of the algebra of functions of a symplectic manifold. Comparison between Fedosov and de Wilde, Lecomte
type: Item
instance of: scholarly article
title: Deformations of the algebra of functions of a symplectic manifold. Comparison between Fedosov and de Wilde, Lecomte
zbMATH Open document ID: 0852.58033
DOI: 10.1007/BF01587907
published in: Selecta Mathematica. New Series
publication date: 1996-11-26T00:00:00Z
review text: \textit{M. de Wilde} and \textit{P. B. A. Lecomte} in their papers in Ann. Inst. Fourier 35, No. 2, 117-143 (1985; Zbl 0526.58023), Lett. Math. Phys. 7, 487-496 (1983; Zbl 0566.58039) and \textit{B. V. Fedosov} in his paper ``Formal quantization'' [Some topics of Modern Mathematics and their applications to problems of mathematical physics, Moscow, 129-136 (1985)] have proved that if \(M\) is a symplectic manifold, then there exists a deformation \(*_t\) of the product giving place to the symplectic Poisson brackets. The classifications of the classes of isomorphy of the above deformations \(*_t\) are given by Fedosov and also by De Wilde and Lecomte. The purpose of the present paper is to compare the applied methods, the corresponding classifications and also to explain the effect of a change of formal parameter \(t \to \sum^\infty_1 a_nt^n\) with \(a_1\) invertible.
Mathematics Subject Classification ID: 53D55
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53D17
zbMATH DE Number: 894937
zbMATH Keywords: symplectic manifold
zbMATH Keywords: deformation
zbMATH Keywords: symplectic Poisson brackets
author: Pierre Deligne
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01587907
OpenAlex ID: W2044575044
description: scientific article; zbMATH DE number 894937