| Reference : Infinite dimensional moment map geometry and closed Fedosov star products |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/37311 | |||
| Infinite dimensional moment map geometry and closed Fedosov star products | |
| English | |
La Fuente-Gravy, Laurent  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| 2016 | |
| Annals of Global Analysis and Geometry | |
| Kluwer Academic Publishers | |
| 49 | |
| 1 | |
| 1-22 | |
| Yes (verified by ORBilu) | |
| International | |
| 0232-704X | |
| 1572-9060 | |
| Netherlands | |
| [en] symplectic connections ; closed star product ; moment map ; deformation quantization ; Kähler manifolds | |
| [en] We study the Cahen–-Gutt moment map on the space of symplectic connections of a
symplectic manifold. Given a Kähler manifold (M, ω, J ), we define a Calabi-type functional F on the space M of Kähler metrics in the class [ω]. We study the space of zeroes of F. When (M, ω, J ) has non-negative Ricci tensor and ω is a zero of F, we show the space of zeroes of F near ω has the structure of a smooth finite dimensional submanifold. We give a new motivation, coming from deformation quantization, for the study of moment maps on infinite dimensional spaces. More precisely, we establish a strong link between trace densities for star products (obtained from Fedosov-type methods) and moment map geometry on infinite dimensional spaces. As a byproduct, we provide, on certain Kähler manifolds, a geometric characterization of a space of Fedosov star products that are closed up to order 3. | |
| Researchers | |
| http://hdl.handle.net/10993/37311 | |
| 10.1007/s10455-015-9477-x |
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