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Cohomologie tangente et cup-produit pour la quantification de Kontsevich

Dominique ManchonCharles Torossian — 2003

Annales mathématiques Blaise Pascal

On a flat manifold M = d , M. Kontsevich’s formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that for any formal Poisson 2 -tensor γ the derivative at γ of the quasi-isomorphism induces an isomorphism of graded commutative algebras from Poisson cohomology space to Hochschild cohomology space relative to the deformed multiplication built from γ via the quasi-isomorphism. We give here a detailed proof of this result, with signs and orientations precised....

Quantification pour les paires symétriques et diagrammes de Kontsevich

Alberto S. CattaneoCharles Torossian — 2008

Annales scientifiques de l'École Normale Supérieure

In this article we use the expansion for biquantization described in [7] for the case of symmetric spaces. We introduce a function of two variables E ( X , Y ) for any symmetric pairs. This function has an expansion in terms of Kontsevich’s diagrams. We recover most of the known results though in a more systematic way by using some elementary properties of this E function. We prove that Cattaneo and Felder’s star product coincides with Rouvière’s for any symmetric pairs. We generalize some of Lichnerowicz’s...

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