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Formal Symplectic Groupoid of a Deformation Quantization

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Abstract

We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique formal symplectic groupoid ‘with separation of variables’ over an arbitrary Kähler-Poisson manifold.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Abilene Christian University, ACU Box 28012, 252 Foster Science Building, Abilene, TX, 79699-8012, USA

    Alexander V. Karabegov

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  1. Alexander V. Karabegov
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Correspondence to Alexander V. Karabegov.

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Communicated by L. Takhtajan

Research was partially supported by an ACU Math/Science grant.

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Karabegov, A. Formal Symplectic Groupoid of a Deformation Quantization. Commun. Math. Phys. 258, 223–256 (2005). https://doi.org/10.1007/s00220-005-1336-3

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  • DOI: https://doi.org/10.1007/s00220-005-1336-3

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