Related papers: Strict quantization of polynomial Poisson structur…

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…

In this note, we study Schwarz's conjecture on application of Q-algebras to strict quantization. We prove that in the case of a torus with a constant Poisson structure, Schwarz's formalism gives the same star product as Rieffel…

Starting from formal deformation quantization we use an explicit formula for a star product on the Poincar\'e disk D_n to introduce a Fr\'echet topology making the star product continuous. To this end a general construction of locally…

One way of reconciling classical and quantum mechanics is deformation quantization, which involves deforming the commutative algebra of functions on a Poisson manifold to a non-commutative, associative algebra, reminiscent of the space of…

We extend the notion of Morita equivalence of Poisson manifolds to the setting of {\em formal} Poisson structures, i.e., formal power series of bivector fields $\pi=\pi_0 + \lambda\pi_1 +\cdots$ satisfying the Poisson integrability…

An analogue of the Moyal star product is presented for the deformed oscillator algebra. It contains several homotopy-like additional integration parameters in the multiplication kernel generalizing the differential Moyal star-product…

Using a derivative decomposition of the Hochschild differential complex we define a generalized inverse of the Hochschild coboundary operator. It can be applied for systematic computations of star products on Poisson manifolds.

We develop a theory of short star-products for filtered quantizations of graded Poisson algebras, introduced in 2016 by Beem, Peelaers and Rastelli for algebras of regular functions on hyperK\"ahler cones in the context of 3-dimensional…

Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd. We exhibit in…

We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces,…

A proposed definition is given for the quantization of a Poisson algebra, taking the quantum product to be a geodesic on the manifold of associative products.

Motivated by deformation quantization we consider $^*$-algebras over ordered rings and their deformations: we investigate formal associative deformations compatible with the $^*$-involution and discuss a cohomological description in terms…

We develop a complete theory of non-formal deformation quantization on the cotangent bundle of a weakly exponential Lie group. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…

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…

We give a geometric method for determining the cohomology groups and the product structure of a polyhedral product, under suitable freeness conditions or with coefficients taken in a field. This is done by considering first a special class…

We construct and classify all Poisson structures on quasimodular forms that extend the one coming from the first Rankin-Cohen bracket on the modular forms. We use them to build formal deformations on the algebra of quasimodular forms.

We prove estimates at infinity of convolutions $f^{n\star}$ and densities of the corresponding compound Poisson measures for a class of radial decreasing densities on $\mathbb{R}^d$, $d \geq 1$, which are not convolution equivalent.…

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 construct a large collection of "quantum projective spaces", in the form of Koszul, Calabi-Yau algebras with the Hilbert series of a polynomial ring. We do so by starting with the toric ones (the q-symmetric algebras), and then deforming…

The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under…