Reference : On deformation quantization of quadratic Poisson structures
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/48462
On deformation quantization of quadratic Poisson structures
English
Merkoulov (merkulov), Serguei mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Khoroshkin, Anton [High School of Economics > Mathematics]
2021
No
[en] Deformation quantization ; Poisson geometry ; graph complexes
[en] 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-Teichm├╝ller group acts on the genus completion of that wheeled properad faithfully and essentially transitively. As a second application we classify all universal quantizations of Z-graded quadratic Poisson structures together with the underlying (so called) homogeneous formality maps.
http://hdl.handle.net/10993/48462
https://arxiv.org/abs/2109.07793

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