deformation quantization; Hitchin connection; star products
Résumé :
[en] We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection defined in. We establish a necessary and sufficient condition that guarantees the existence of a formal connection, and we describe the space of formal connections for a family as an affine space modelled by the derivations of the star products. Moreover we show that if the parameter space has trivial first cohomology group any two flat formal connections are related by an automorphism of the family of star products.
Centre de recherche :
Center of Quantum Geometry of Moduli Spaces, Aarhus University (Aarhus, Denmark)
Disciplines :
Mathématiques
Auteur, co-auteur :
Andersen, Joergen; Aarhus Universitet - AU > Department of Mathematics > Professor
Masulli, Paolo; University of Lausanne (Lausanne, Switzerland) > Faculty of Business and Economics (HEC) and Faculty of Law, Criminal Justice and Public Administration (FDCA) > postdoc
SCHATZ, Florian ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
