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Bieliavsky, Pierre; Esposito, Chiara; Waldmann, Stefan; Weber, Thomas

Obstructions for twist star products. (English) Zbl 1392.53082

Lett. Math. Phys. 108, No. 5, 1341-1350 (2018).
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.
Reviewer: Angela Gammella-Mathieu (Metz)

Cited in 5 Documents

MSC:

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

Keywords:

deformation quantization; Poisson structure; twist star products; \(r\)-matrix; symplectic Pretzel surfaces; symplectic spheres
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\textit{P. Bieliavsky} et al., Lett. Math. Phys. 108, No. 5, 1341--1350 (2018; Zbl 1392.53082)
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