On deformation quantization of quadratic Poisson structures

2021/09/16 by Anton Khoroshkin, Khoroshkin, Anton, Sergei Merkulov +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2109.07793

openalex publication_date 2021/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

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