2016/11/15 by Derek Krepski, Krepski, Derek
Mathematics · #53C08 #53D17 #53D20 #53D50 #58H05 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53C08 #msc:53D17 #msc:53D20 #msc:53D50 #msc:58H05
paper · pdf · doi:10.48550/arxiv.1611.04711
28 pages
arxiv created 2016/11/15 · arxiv updated 2016/11/16
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.