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Quantization of Symplectic Dynamical r-Matrices and the Quantum Composition Formula

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Abstract

In this paper we quantize symplectic dynamical r-matrices over a possibly nonabelian base. The proof is based on the fact that the existence of a star-product with a nice property (called strong invariance) is sufficient for the existence of a quantization. We also classify such quantizations and prove a quantum analogue of the classical composition formula for coboundary dynamical r-matrices.

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Author notes

  1. Damien Calaque

    Present address: Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622, Villeurbanne cedex, France

Authors and Affiliations

  1. Section de Mathématiques (UNIGE), 2-4 rue du Lièvre, 1211, Genève, Switzerland

    Anton Alekseev

  2. Max Planck Institüt für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany

    Damien Calaque

Authors
  1. Anton Alekseev
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  2. Damien Calaque
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Correspondence to Damien Calaque.

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Communicated by L. Takhtajan

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Alekseev, A., Calaque, D. Quantization of Symplectic Dynamical r-Matrices and the Quantum Composition Formula. Commun. Math. Phys. 273, 119–136 (2007). https://doi.org/10.1007/s00220-007-0245-z

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  • DOI: https://doi.org/10.1007/s00220-007-0245-z

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