# On deformation quantization of quadratic Poisson structures

@inproceedings{Khoroshkin2021OnDQ, title={On deformation quantization of quadratic Poisson structures}, author={Anton Khoroshkin and Sergei Merkulov}, year={2021} }

We study the deformation complex of the dg wheeled properad of Z-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the Grothendieck-Teichmüller group acts on the genus completion of that wheeled properad faithfully and essentially transitively. As a second application we classify all the universal quantizations of Z-graded quadratic Poisson structures (together with the underlying homogeneous… Expand

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