Universal enveloping algebras and quantization

Grabowski, Janusz

Displaying similar documents to “Universal enveloping algebras and quantization”

Poisson-Nijenhuis structures

Yvette Kosmann-Schwarzbach, Franco Magri (1990)

Annales de l'I.H.P. Physique théorique

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Linearization and star products

Veronique Chloup (2000)

Banach Center Publications

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The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.

Hochschild cohomology and quantization of Poisson structures

Grabowski, Janusz

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It is well-known that the question of existence of a star product on a Poisson manifold $N$ is open and only some partial results are known [see the author, J. Geom. Phys. 9, No. 1, 45-73 (1992; Zbl 0761.16012)].In the paper under review, the author proves the existence of the star products for the Poisson structures $P$ of the following type $P = X \land Y$ with $[X, Y] = u X + v Y$ , for some $u, v \in C^{\infty} (N, ℝ)$ .