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.


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