Letters in Mathematical Physics

, Volume 108, Issue 5, pp 1341–1350 | Cite as

Obstructions for twist star products

  • Pierre Bieliavsky
  • Chiara Esposito
  • Stefan Waldmann
  • Thomas Weber


In this short note, we point out that not every star product is induced by a Drinfel’d twist by showing that not every Poisson structure is induced by a classical r-matrix. Examples include the higher genus symplectic Pretzel surfaces and the symplectic sphere \({\mathbb {S}}^2\).

Mathematics Subject Classification

53D05 53D55 22F30 22E60 57S25 



We would like to thank Martin Bordemann, Alexander Schenkel and Jonas Schnitzer for valuable discussions and useful suggestions.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Faculté des sciences, Ecole de mathématique (MATH)Institut de recherche en mathématique et physique (IRMP)Louvain-la-NeuveBelgium
  2. 2.Institut für Mathematik, Lehrstuhl für Mathematik XUniversität WürzburgWürzburgGermany

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