On Deformation Quantization of Quadratic Poisson Structures

Anton Khoroshkin, Sergei Merkulov

Research output: Contribution to journalArticlepeer-review


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 formality maps). In particular we show that two universal quantizations of Poisson structures are equivalent if the agree on generic quadratic Poisson structures.

Original languageEnglish
Pages (from-to)597-628
Number of pages32
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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