Special symplectic connections and Poisson geometry (Q703991)

The authors show how any special symplectic connection can be constructed using symplectic realizations of quadratic deformations of a certain linear Poisson structure. The space of symplectic connections is rather huge. Therefore, to study meaningful connections, it is thus necessary to impose further conditions. In this paper, the authors investigate the so-called special symplectic connections. They first recall the various conditions of such symplectic connections and their relevance. They also review the standard results and notions related both to symplectic and Poisson geometry, and symplectic groupoids. Then they prove the main result of the paper. Finally, some general consequences are discussed.