Reference : Formal connections for families of star products
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Formal connections for families of star products
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 mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Communications in Mathematical Physics
Springer Science & Business Media B.V.
Yes (verified by ORBilu)
[en] deformation quantization ; Hitchin connection ; star products
[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.
Center of Quantum Geometry of Moduli Spaces, Aarhus University (Aarhus, Denmark)
Danish National Research Foundation by the Center of excellence grant ’Centre for Quantum Geometry of Moduli Spaces’ (DNRF 95
The article appeared online originally at

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