Related papers: Projectively and conformally invariant star-produc…

Global properties of abelian noncommutative gauge theories based on $\star$-products which are deformation quantizations of arbitrary Poisson structures are studied. The consistency condition for finite noncommutative gauge transformations…

Based on a closed formula for a star product of Wick type on $\CP^n$, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra (with coefficients contained in the…

We study quantum deformations of Poisson orbivarieties. Given a Poisson manifold $(\mathbb{R}^{m},\alpha)$ we consider the Poisson orbivariety $(\mathbb{R}^{m})^{n}/S_{n}$. The Kontsevich star product on functions on $(\mathbb{R}^{m})^{n}$…

We give an explicit formula for the decomposition of the tensor product of any two indecomposable non-projective modules for the symmetric group algebra $F \mathfrak{S}_p$ modulo projective modules. In particular, we show that the tensor…

We present a deformed star-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization-dequantization scheme, with the correspondence between classical observables and operators…

Let X be a CW complex with a continuous action of a topological group G. We show that if X is equivariantly formal for singular cohomology with coefficients in a field, then so are all symmetric products of X and in fact all its…

We present a friendly introduction to the very detailed results in [9,10,11] and as an illustration we discuss here the issue of {\em linearization of products}. We find some interesting new phenomena.

We deal with smooth real manifolds as well as complex analytic manifolds as well. It is well known that the concept of star product is powerful enough to produce all Poisson structures on real manifolds. According to [BdM] it is not known…

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we…

After a brief description of the $\mathbb{Z}$-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter…

We construct a $U_q(\mathrm{so}(2n+1))$-equivariant local star-product on the complex sphere $\mathbb{S}^{2n}$ as a Non-Levi conjugacy class $SO(2n+1)/SO(2n)$.

A differential geometric version of noncommutative topological index theorem is worked out for covariant star products on noncommutative vector bundles. For start, a noncommutative manifold is considered as a product space X = Y * Z,…

In this note, we provide a proof of the existence and complete classification of $G$-invariant star products with quantum momentum maps on Poisson manifolds by means of an equivariant version of the formality theorem.

We prove the following variant of Marstrand's theorem about projections of cartesian products of sets: Let $K_1,...,K_n$ Borel subsets of $\mathbb R^{m_1},... ,\mathbb R^{m_n}$ respectively, and $\pi:\mathbb R^{m_1}\times...\times\mathbb…

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…

We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. This way symmetry…

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…

Given a mechanical system $(M, \mathcal{F}(M))$, where $M$ is a Poisson manifold and $\mathcal{F}(M)$ the algebra of regular functions on $M$, it is important to be able to quantize it, in order to obtain more precise results than through…

We construct a family of fermionic star products generalising the fermionic Moyal product. The parameter space contains the polarisations necessary to define a quantum Hilbert space. We find a star product of fermionic functions on sections…

We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique…