Invariant star-products on symplectic manifolds
type: Item
instance of: scholarly article
title: Invariant star-products on symplectic manifolds
zbMATH Open document ID: 0589.53036
DOI: 10.1016/0393-0440(85)90022-1
author: Marc De Wilde
author: Pierre B. A. Lecomte
author: D. Melotte
published in: Journal of Geometry and Physics
publication date: 1985-01-01T00:00:00Z
review text: Considering a Lie subalgebra G of the Lie algebra of symplectic vector fields on a symplectic manifold (M,F), the authors prove that every one- differentiable deformation of order k of the Poisson Lie algebra of M, which is invariant with respect to G, extends to an invariant one- differentiable deformation of infinite order. In particular, if M admits a G-invariant linear connection, a similar result holds for differentiable deformations and for star-products. In this case there always exists a G-invariant star-product.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 3947103
zbMATH Keywords: symplectic vector fields
zbMATH Keywords: symplectic manifold
zbMATH Keywords: differentiable deformation
zbMATH Keywords: G-invariant linear connection
zbMATH Keywords: star-product
reviewed by: Vasile Cruceanu
MaRDI profile type: Publication
full work available at URL: 0393-0440(85)90022-1
OpenAlex ID: W2108384146
cites work: Covariance and geometrical invariance in *quantization
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cites work: Déformations d'algèbres associées à une variété symplectique (les \(*_\nu\)-produits)
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cites work: Déformation du crochet de Poisson sur une variété symplectique
description: scientific article; zbMATH DE number 3947103