Reference : The formal moment map geometry of the space of symplectic connections
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/47853
The formal moment map geometry of the space of symplectic connections
English
La Fuente-Gravy, Laurent mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Jun-2021
No
[en] We deform the moment map picture on the space of symplectic connections on a symplectic manifold. To do that, we study a vector bundle of Fedosov star product algebras on the space of symplectic connections. We describe a natural formal connection on this bundle adapted to the star product algebras on the fibers. We study its curvature and show the star product trace of the curvature is a formal symplectic form on the space of symplectic connections. The action of Hamiltonian diffeomorphisms on symplectic connections preserves the formal symplectic structure and we show the star product trace can be interpreted as a formal moment map for this action. Finally, we apply this picture to study automorphisms of star products and Hamiltonian diffeomorphisms.
http://hdl.handle.net/10993/47853
https://arxiv.org/abs/2106.13608

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