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Obstructions for twist star products

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Abstract

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 \({\mathbb {S}}^2\).

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Acknowledgements

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

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Authors and Affiliations

  1. Faculté des sciences, Ecole de mathématique (MATH), Institut de recherche en mathématique et physique (IRMP), Chemin du Cyclotron 2 bte L7.01.02, 1348, Louvain-la-Neuve, Belgium

    Pierre Bieliavsky

  2. Institut für Mathematik, Lehrstuhl für Mathematik X, Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Straße 31, 97074, Würzburg, Germany

    Chiara Esposito, Stefan Waldmann & Thomas Weber

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  1. Pierre Bieliavsky
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  2. Chiara Esposito
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  3. Stefan Waldmann
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  4. Thomas Weber
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Correspondence to Chiara Esposito.

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Bieliavsky, P., Esposito, C., Waldmann, S. et al. Obstructions for twist star products. Lett Math Phys 108, 1341–1350 (2018). https://doi.org/10.1007/s11005-017-1034-z

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  • DOI: https://doi.org/10.1007/s11005-017-1034-z

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