Displaying similar documents to “Hochschild cohomology and quantization of Poisson structures”

Logarithmic Poisson cohomology: example of calculation and application to prequantization

Joseph Dongho (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure. We prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kähler differentials. Therefore it induces a differential complex from which we derive the notion of logarithmic Poisson cohomology. We prove that Poisson cohomology and logarithmic Poisson cohomology are equal when the Poisson structure is log symplectic. We give an...

Associative and Lie deformations of Poisson algebras

Elisabeth Remm (2012)

Communications in Mathematics

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Considering a Poisson algebra as a nonassociative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this nonassociative algebra. We give a natural interpretation of deformations which preserve the underlying associative structure and of deformations which preserve the underlying Lie algebra and we compare the associated cohomologies with the Poisson cohomology parametrizing the general deformations of Poisson algebras.

Classifications of star products and deformations of Poisson brackets

Philippe Bonneau (2000)

Banach Center Publications

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On the algebra of functions on a symplectic manifold we consider the pointwise product and the Poisson bracket; after a brief review of the classifications of the deformations of these structures, we give explicit formulas relating a star product to its classifying formal Poisson bivector.

Universal enveloping algebras and quantization

Grabowski, Janusz

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It is shown how the universal enveloping algebra of a Lie algebra L can be obtained as a formal deformation of the Kirillov-Souriau Poisson algebra C ∞ ( L * ) of smooth functions on the dual of L . This deformation process may be viewed as a “quantization” in the sense of and [Ann. Phys. 111, 61-110 (1978; Zbl 0377.53024) and ibid., 111-151 (1978; Zbl 0377.53025)]. The result presented is a somewhat more elaborate version of earlier findings by [Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019)]...