## Obstructions for twist star products.(English)Zbl 1392.53082

This paper studies obstructions for a given star product to be induced by a twist. First, the authors recall the main notions and results about Drinfel’d twist and classical $$r$$-matrix. Then, they prove that not every Poisson structure is induced by a classical $$r$$-matrix. Counterexamples are obtained by symplectic manifolds which are not homogeneous and by higher-genus Pretzel surfaces or by the sphere.

### MSC:

 53D05 Symplectic manifolds (general theory) 53D55 Deformation quantization, star products
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### References:

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