[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-Teichmüller 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.
Disciplines :
Mathematics
Author, co-author :
MERKOULOV (MERKULOV), Serguei ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Khoroshkin, Anton; High School of Economics > Mathematics
External co-authors :
yes
Language :
English
Title :
On deformation quantization of quadratic Poisson structures