Related papers: Coherent Quantization using Coloured Surfaces

We quantize the Poisson-Lie group SL(2,R)^* as a bialgebra using the product of Kontsevich. The coproduct is a deformation of the coproduct that comes from the group structure. The resulting bialgebra structure is isomorphic to the quantum…

We propose a generalization of quantization as a categorical way. For a fixed Poisson algebra quantization categories are defined as subcategories of R-module category with the structure of classical limits. We construct the generalized…

We formulate a notion of $E_{-1}$ quantisation of $(-2)$-shifted Poisson structures on derived algebraic stacks, depending on a flat right connection on the structure sheaf, as solutions of a quantum master equation. We then parametrise…

We call a finite-dimensional complex Lie algebra $\mathfrak{g}$ strongly rigid if its universal enveloping algebra $\Ug$ is rigid as an associative algebra, i.e. every formal associative deformation is equivalent to the trivial deformation.…

We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix…

We present a geometric construction of central S^1-extensions of the quantomorphism group of a prequantizable, compact, symplectic manifold, and explicitly describe the corresponding lattice of integrable cocycles on the Poisson Lie…

We classify deformation quantizations of the symplectic supervarieties that are smooth and admissible. This generalizes the corresponding result of Bezrukavnikov and Kaledin to the super case. We relate the equivalence classes of…

To any field K of characteristic 0, we associate a set Sha(K). Elements of Sha(K) are equivalence classes of families of Lie polynomials subject to associativity relations. We construct an injection and a retraction between Sha(K) and the…

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…

We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The…

In this work, we find the Poisson superalgebras related to schemes of quantization. Initially, we consider the Dirac superbracket in the context of the quantization of constrained systems. Next, we show the existence of a Poisson…

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 construct explicitly a class of coboundary Poisson-Lie structures on the group of formal diffeomorphisms of ${\Bbb R}^n$. Equivalently, these give rise to a class of coboundary triangular Lie bialgebra structures on the Lie algebra $W_n$…

We explain how to translate several recent results in derived algebraic geometry to derived differential geometry. These concern shifted Poisson structures on NQ-manifolds, Lie groupoids, smooth stacks and derived generalisations, and…

Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…

We give an algebraic quantization, in the sense of quantum groups, of the complex Minkowski space, and we examine the real forms corresponding to the signatures $(3,1)$, $(2,2)$, $(4,0)$, constructing the corresponding quantum metrics and…

This paper studies differential graded modules and representations up to homotopy of Lie $n$-algebroids, for general $n\in\mathbb{N}$. The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and…

An analogue of geometric quantization of Poisson algebras obtained by algebraic reduction of symmetries is developed. Interpretation of the obtained results and their application to the problem of commutativity of quantization and reduction…

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…

We canonically quantize a Poisson manifold to a Lie 2-groupoid, complete with a quantization map, and show that it relates geometric and deformation quantization: the perturbative expansion in $\hbar$ of the (formal) convolution of two…