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24 April 2024 |
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Groupoid equivariant prequantization | | Derek Krepski
; | | Date: |
15 Nov 2016 | | 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
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-presymplectic structure is exact. Properties related to Morita invariance
and symplectic reduction are established. | | Source: | arXiv, 1611.4711 | | Services: | Forum | Review | PDF | Favorites | |
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