Autour des déformations de Rankin-Cohen.

Abstract : In this thesis aims to study the Rankin-Cohen brackets and the corresponding deformation according to different points of view. We present a new interpretation of a side strain Rankin-Cohen via the theory of "deformation quantization of Fedosov (in collaboration with P. Bieliavsky and X. Tang). It manages to include a new proof of Connes-Moscovici theorem on formal deformation of algebras under the action of a Hopf algebra equipped with a H1 projective structure. From the other side is given in Chapter III contains a detailed interpretation of Rankin-Cohen brackets via the theory of unitary representations of SL2 (R) and using this interpretation we study some properties of warped products, including unique products manufactured by Cohen-Manin-Zagier and a separation property of the product Eholzer. In the final chapter gives a basic demonstration combinatorial identity that is crucial to demonstrate associativity in the approach to the issue of deformation by Cohen-Manin-Zagier, Eholzer, and Connes-Moscovici.
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Yi-Jun Yao. Autour des déformations de Rankin-Cohen.. Mathématiques [math]. Ecole Polytechnique X, 2007. Français. ⟨pastel-00002414⟩

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