Integration of twisted Dirac brackets
Given a Lie groupoid G over a manifold M, we show that multiplicative 2-forms on G relatively closed with respect to a closed 3-form ϕ; on M correspond to maps from the Lie algebroid of G into T * M satisfying an algebraic condition and a differential condition with respect to the ϕ-twisted Courant...
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| Veröffentlicht in: | Duke mathematical journal 2004-06, Vol.123 (3), p.549-607 |
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| container_issue | 3 |
| container_start_page | 549 |
| container_title | Duke mathematical journal |
| container_volume | 123 |
| creator | Bursztyn, Henrique Crainic, Marius Weinstein, Alan Zhu, Chenchang |
| description | Given a Lie groupoid G over a manifold M, we show that multiplicative 2-forms on G relatively closed with respect to a closed 3-form ϕ; on M correspond to maps from the Lie algebroid of G into T * M satisfying an algebraic condition and a differential condition with respect to the ϕ-twisted Courant bracket. This correspondence describes, as a special case, the global objects associated to ϕ-twisted Dirac structures. As applications, we relate our results to equivariant cohomology and foliation theory, and we give a new description of quasi-Hamiltonian spaces and group-valued momentum maps. |
| doi_str_mv | 10.1215/S0012-7094-04-12335-8 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0012-7094 |
| ispartof | Duke mathematical journal, 2004-06, Vol.123 (3), p.549-607 |
| issn | 0012-7094 1547-7398 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1086957716 |
| source | Project Euclid Complete |
| subjects | 22E65 53C12 53D17 53D20 57R32 58H05 Foliations (differential geometric aspects) [See also 57R30 Momentum maps Poisson groupoids and algebroids Poisson manifolds Pseudogroups and differentiable groupoids [See also 22A22 symplectic reduction |
| title | Integration of twisted Dirac brackets |
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