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Hochschild cohomology and quantization of Poisson structures. (English) Zbl 0836.58016
Bureš, J. (ed.) et al., Proceedings of the winter school on geometry and physics, Zdíkov, Czech Republic, January 1993. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 37, 87-91 (1994).
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 $$P= X\wedge Y$$ with $$[X, Y]= uX+ vY$$, for some $$u,v\in C^\infty(N,\mathbb{R})$$.
For the entire collection see [Zbl 0823.00015].

##### MSC:
 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 53D50 Geometric quantization 17B65 Infinite-dimensional Lie (super)algebras 17B56 Cohomology of Lie (super)algebras 16S80 Deformations of associative rings
##### Keywords:
Poisson structures; star product; quantization