Communications in Mathematical Physics

, Volume 342, Issue 2, pp 739–768 | Cite as

Formal Connections for Families of Star Products

  • Jørgen Ellegaard Andersen
  • Paolo Masulli
  • Florian Schätz


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, which was introduced by the first author. 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 on the formal symplectic vector fields. Moreover, we showthat 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.


Modulus Space Toeplitz Operator Symplectic Manifold Formal Power Series Star Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jørgen Ellegaard Andersen
    • 1
  • Paolo Masulli
    • 1
  • Florian Schätz
    • 1
  1. 1.Centre for Quantum Geometry of Moduli SpacesAarhus UniversityAarhus CDenmark

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