Corpus ID: 237532272

On deformation quantization of quadratic Poisson structures

@inproceedings{Khoroshkin2021OnDQ,
  title={On deformation quantization of quadratic Poisson structures},
  author={Anton Khoroshkin and Sergei Merkulov},
  year={2021}
}
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… Expand

References

SHOWING 1-10 OF 39 REFERENCES
From Deformation Theory of Wheeled Props to Classification of Kontsevich Formality Maps
We study homotopy theory of the wheeled prop controlling Poisson structures on arbitrary formal graded finite-dimensional manifolds and prove, in particular, that Grothendieck-Teichmueller group actsExpand
Graph Complexes with Loops and Wheels
Motivated by the problem of deformation quantization we introduce and study directed graph complexes with oriented loops and wheels – differential graded (dg) wheeled props. We develop a newExpand
PROP Profile of Poisson Geometry
It is shown that some classical local geometries are of infinity origin, i.e. their smooth formal germs are (homotopy) representations of cofibrant (di) operads in spaces concentrated in degree zero.Expand
Double Poisson algebras
In this paper we develop Poisson geometry for non-commutative algebras. This generalizes the bi-symplectic geometry which was recently, and independently, introduced by Crawley-Boevey, Etingof andExpand
Deformation Quantization of Poisson Manifolds
I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to theExpand
Stable cohomology of polyvector fields
We show that the stable cohomology of the algebraic polyvector fields on $\mathbb{R}^n$, with values in the adjoint representation is the symmetric product space on the cohomology of M. Kontsevich'sExpand
Deformation theory of representations of prop(erad)s I
Abstract In this paper and its follow-up [Merkulov and Vallette, J. reine angew. Math.], we study the deformation theory of morphisms of properads and props thereby extending Quillen's deformationExpand
Deformation theory of bialgebras, higher Hochschild cohomology and Formality
A first goal of this paper is to precisely relate the homotopy theories of bialgebras and E 2-algebras. For this, we construct a conservative and fully faithful ∞-functor from pointed conilpotentExpand
Deformation Theory of Lie Bialgebra Properads
This chapter presents the homotopy derivations of the properads governing even and odd Lie bialgebras, as well as involutive Lie bialgebras. The answer may be expressed in terms of the KontsevichExpand
Geometry and quantization
Gravity is treated geometrically in terms of nonlinear realizations ofGL(4, ℝ) with particular reference to almost complex structures. This approach is used to carry out a Bargmann-Segal typeExpand
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