Existence of star-products on exact symplectic manifolds

DOI10.5802/aif.1013zbMath0536.58038OpenAlexW2051684319MaRDI QIDQ791956

Pierre B. A. Lecomte, Marc De Wilde

Publication date: 1984

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1985__35_2_117_0

zbMATH Keywords

Hochschild cohomologyPoisson Lie algebraChevalley cohomology

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) (58H10) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items

Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds, Deformations of the algebra of functions of a symplectic manifold. Comparison between Fedosov and de Wilde, Lecomte, An exterior calculus for exact symplectic manifolds, Unnamed Item, Lagrange–Fedosov nonholonomic manifolds, Constructions of noncommutative instantons on \(\mathbb{T}^4\) and \(K_3\), Fedosov manifolds

Cites Work

• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• Regular * representations of Lie algebras
• Sur les algèbres formelles associees par déformation à une variété symplectique
• Déformations d'algèbres associées à une variété symplectique (les \(*_\nu\)-produits)
• Cohomology of the Lie algebra of smooth vector fields of a manifold, associated to the Lie derivative of smooth forms
• Déformation du crochet de Poisson sur une variété symplectique
• Deformation theory and quantization. I: Deformations of symplectic structures
• Sur l'algèbre des automorphismes infinitesimaux d'une variété symplectique
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