XXXIV Workshop on Geometric Methods in Physics | 28.06-4.07.2015 |

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## MichaĆ Dobrski## Generalized Fedosov algebras and noncommutative gravitySimple generalization of Fedosov construction based on fairly general (not necessarily Moyal) fiberwise star product in the Weyl bundle will be presented. The construction is motivated by a possible application in noncommutative field theory, particularly in noncommutative gravity. The basic idea of this application is to introduce the spacetime metric into the deformation quantization scheme from the very begining, as the "symmetric part of the noncommutativity tensor". It turns out, that such approach can be covered by the considered generalization. Remarks on some particular noncommutative gravity model built within this framework will be provided. |

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