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Groupoid Equivariant Prequantization

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Abstract

In their 2005 paper, C. Laurent-Gengoux and P. Xu define prequantization for pre-Hamiltonian actions of quasi-presymplectic Lie groupoids in terms of S1-central extensions of Lie groupoids. The definition requires that the quasi-presymplectic structure be exact (i.e., the closed 3-form on the unit space of the Lie groupoid must be exact). In the present paper, we define prequantization for pre-Hamiltonian actions of (not necessarily exact) quasi-presymplectic Lie groupoids in terms of Dixmier–Douady bundles. The definition is a natural adaptation of E. Meinrenken’s treatment of prequantization for quasi-Hamiltonian Lie group actions with group-valued moment map. The definition given in this paper is shown to be compatible with the definition of Laurent-Gengoux and Xu when the underlying quasi-preysmplectic structure is exact. Properties related to Morita invariance and symplectic reduction are established.

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Authors and Affiliations

  1. Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada

    Derek Krepski

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  1. Derek Krepski
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Correspondence to Derek Krepski.

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Communicated by C. Schweigert

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Krepski, D. Groupoid Equivariant Prequantization. Commun. Math. Phys. 360, 169–195 (2018). https://doi.org/10.1007/s00220-017-3080-x

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