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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)].\par 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 $u,v\in C^\infty(N,\bbfR)$.
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