Related papers: Poisson bracket, deformed bracket and gauge group …
Global constructions of quantization deformation and obstructions are discussed for an arbitrary complex analytic space in terms of adapted (analytic) Hochschild cohomology. For K3-surfaces an explicit global construction of a Poisson…
On the basis of the quantum q-oscillator algebra in the framework of quantum groups and non-commutative q-differential calculus, we investigate a possible q-deformation of the classical Poisson bracket in order to extend a generalized…
It is known that, for the algebra of functions on a Kleinian singularity, the parameter space of deformations and the parameter space of quantizations coincide. We prove that, for a Kleinian singularity of type $\mathbf{A}$ or $\mathbf{D}$,…
These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
Kontsevich constructed a map between `good' graph cocycles $\gamma$ and infinitesimal deformations of Poisson bivectors on affine manifolds, that is, Poisson cocycles in the second Lichnerowicz--Poisson cohomology. For the tetrahedral graph…
On a foliated manifold equipped with an action of a compact Lie group $G$, we study a class of almost-coupling Poisson and Dirac structures, in the context of deformation theory and the method of averaging.
This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L-infinity…
A Hamiltonian formulation of gauge symmetries on noncommutative ($\theta$ deformed) spaces is discussed. Both cases- star deformed gauge transformation with normal coproduct and undeformed gauge transformation with twisted coproduct- are…
In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized Verma module to quantize the Kirillov bracket…
In this note the notion of Poisson brackets in Kontsevich's "Lie World" is developed. These brackets can be thought of as "universally" defined classical Poisson structures, namely formal expressions only involving the structure maps of a…
We show that every star product on a symplectic manifold defines uniquely a 1-differentiable deformation of the Poisson bracket. Explicit formulas are given. As a corollary we can identify the characteristic class of any star product as a…
Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of integration on these moduli spaces via…
A class of nongraded Hamiltonian Lie algebras was earlier introduced by Xu. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a ``sandwich'' method…
We prove the existence of a deformation quantization for integrable Poisson structures on R^3 and give a generalization for a special class of three dimensional manifolds.
In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic…
We consider the space of bilinear forms on a complex N-dimensional vector space endowed with the quadratic Poisson bracket studied in our previous paper arXiv:1012.5251. We classify all possible quadratic brackets on the set of pairs of…
Given a formal symplectic groupoid $G$ over a Poisson manifold $(M, \pi_0)$, we define a new object, an infinitesimal deformation of $G$, which can be thought of as a formal symplectic groupoid over the manifold $M$ equipped with an…
On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears…
Let $M$ be a smooth closed orientable manifold and $\mathcal{P}(M)$ the space of Poisson structures on $M$. We construct a Poisson bracket on $\mathcal{P}(M)$ depending on a choice of volume form. The Hamiltonian flow of the bracket acts on…