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Quantization and Dynamisation of Trace-Poisson Brackets

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Abstract

The quantization problem for the trace-bracket algebra, derived from double Poisson brackets, is discussed. We obtain a generalization of the boundary YBE (or so-called ABCD-algebra) for the quantization of quadratic trace-brackets. A dynamical deformation is proposed on the lines of Gervais–Neveu–Felder dynamical quantum algebras.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, 95302, Cergy-Pontoise, France

    Jean Avan

  2. LAPTh, CNRS and Université de Savoie, 9 Chemin de Bellevue, BP 110, 74941, Annecy le Vieux Cedex, France

    Eric Ragoucy

  3. Laboratoire Angevin de REcherche en MAthématiques (CNRS UMR 6093), UNAM et Université d’Angers, Faculté des Sciences, 2, Boulevard Lavoisier, 49045, Angers Cedex, France

    Vladimir Rubtsov

  4. Theory Division, ITEP, 25, Bol. Tcheremushkinskaya, 117259, Moscow, Russia

    Vladimir Rubtsov

Authors
  1. Jean Avan
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  2. Eric Ragoucy
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  3. Vladimir Rubtsov
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Correspondence to Jean Avan.

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Communicated by N. Reshetikhin

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Avan, J., Ragoucy, E. & Rubtsov, V. Quantization and Dynamisation of Trace-Poisson Brackets. Commun. Math. Phys. 341, 263–287 (2016). https://doi.org/10.1007/s00220-015-2538-y

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  • DOI: https://doi.org/10.1007/s00220-015-2538-y

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