Article (Scientific journals)
On deformation quantization of quadratic Poisson structures
MERKOULOV (MERKULOV), Serguei; Khoroshkin, Anton
2023In Communications in Mathematical Physics, DOI 10.1007/s00220-023-04829-z, p. 1-32
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Keywords :
Deformation quantization; Poisson geometry; graph complexes
Abstract :
[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
Publication date :
October 2023
Journal title :
Communications in Mathematical Physics
ISSN :
0010-3616
eISSN :
1432-0916
Publisher :
Springer, Germany
Volume :
DOI 10.1007/s00220-023-04829-z
Pages :
1-32
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 29 October 2021

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