Related papers: On deformation quantization of quadratic Poisson s…

Motivated by the problem of deformation quantization we introduce and study directed graph complexes with oriented loops and wheels. We develop some technique for computing cohomology of such graph complexes and apply it to several concrete…

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 acts on that wheeled prop faithfully and…

Universal solutions to deformation quantization problems can be conveniently classified by the cohomology of suitable graph complexes. In particular, the deformation quantizations of (finite-dimensional) Poisson manifolds and Lie bialgebras…

In the formulation of his celebrated Formality conjecture, M. Kontsevich introduced a universal version of the deformation theory for the Schouten algebra of polyvector fields on affine manifolds. This universal deformation complex takes…

We extend the author's and CPTVV's correspondence between shifted symplectic and Poisson structures to establish a correspondence between exact shifted symplectic structures and non-degenerate shifted Poisson structures with formal…

We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…

Kontsevich's formula for a deformation quantization of Poisson structures involves a Feynman series of graphs, with the weights given by some complicated integrals (using certain pullbacks of the standard angle form on a circe). We explain…

We study the deformation complex of the standard morphism from the degree $d$ shifted Lie operad to its polydifferential version, and prove that it is quasi-isomorphic to the Kontsevich graph complex $\mathbf{GC}_d$. In particular, we show…

The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent…

We prove that every $0$-shifted Poisson structure on a derived Artin $n$-stack admits a curved $A_{\infty}$ deformation quantisation whenever the stack has perfect cotangent complex; in particular, this applies to LCI schemes, where it…

In recent years, a close connection between supergravity, string effective actions and generalized geometry has been discovered that typically involves a doubling of geometric structures. We investigate this relation from the point of view…

Let X be a smooth affine algebraic variety over a field K of characteristic 0, and let R be a complete parameter K-algebra (e.g. R = K[[h]]). We consider associative (resp. Poisson) R-deformations of the structure sheaf O_X. The set of…

We relate a universal formula for the deformation quantization of arbitrary Poisson structures proposed by Maxim Kontsevich to the Campbell-Baker-Hausdorff formula. Our basic thesis is that exponentiating a suitable deformation of the…

Let $P$ be a Poisson structure on a finite-dimensional affine real manifold. Can $P$ be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach -- with respect to all affine Poisson…

We introduce a new kind of groupoid--a pseudo \'etale groupoid, which provides many interesting examples of noncommutative Poisson algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are…

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We…

We study deformation quantizations of the structure sheaf O_X of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of O_X…

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 the algebra of functions on X is in one-to-one…

We express the difference between Poisson bracket and deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasi-isomorphism. The counterpart on star products of the…

Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely…