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Related papers: Traces for star products on symplectic manifolds

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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…

Quantum Algebra · Mathematics 2009-11-10 Alexander V. Karabegov

It is shown that the normalized trace of Fedosov star product for quantum moment map depends only on the path component in the cohomology class of the symplectic form and the cohomology class of the closed formal 2-form required to define…

Symplectic Geometry · Mathematics 2021-02-24 Akito Futaki , Laurent La Fuente-Gravy

In this paper, we describe all traces for the BCH star-product on the dual of a Lie algebra. First we show by an elementary argument that the BCH as well as the Kontsevich star-product are strongly closed if and only if the Lie algebra is…

Quantum Algebra · Mathematics 2009-11-07 Pierre Bieliavsky , Martin Bordemann , Simone Gutt , Stefan Waldmann

In this note, we prove the existence of one particular class of starshaped compact hypersurfaces, by deriving global curvature estimates for such hypersurfaces; this generalizes the main result in [Hypersurfaces of prescribed mixed…

Differential Geometry · Mathematics 2024-09-24 Bin Wang

We obtain a simple formula for the first-order trace of a regular differential operator on a segment perturbated by a multiplication operator. The main analytic ingredient of the proof is an improvement of the Tamarkin equiconvergence…

Spectral Theory · Mathematics 2016-04-07 Alexander I. Nazarov , Dmitriy M. Stolyarov , Pavel B. Zatitskiy

In this paper we present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S^1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a…

Symplectic Geometry · Mathematics 2015-10-27 Klaus Niederkrüger , Federica Pasquotto

This paper presents a proof of the existence of standard symplectic coordinates near a set of smooth, orthogonally intersecting symplectic submanifolds. It is a generalization of the standard symplectic neighborhood theorem. Moreover, in…

Symplectic Geometry · Mathematics 2018-10-08 Roberta Guadagni

We show, in this note, that on any symplectic supermanifold, even or odd, there exist an infinite dimensional affine space of symmetric connections, compatible to the symplectic form.

Symplectic Geometry · Mathematics 2014-09-11 Paul A. Blaga

We establish various stability results for symplectic surfaces in symplectic $4-$manifolds with $b^+=1$. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify…

Symplectic Geometry · Mathematics 2014-07-07 Josef G. Dorfmeister , Tian-Jun Li , Weiwei Wu

Motivated by and extending the technical results in our earlier work on symplectic Calabi-Yau $4$-manifolds, a general and systematic approach for studying certain unions of symplectic embedded surfaces in a rational $4$-manifold $X=CP^2\#…

Symplectic Geometry · Mathematics 2026-05-20 Weimin Chen

We construct the symplectic resolution of a symplectic orbifold whose isotropy locus consists of disjoint submanifolds with homogeneous isotropy, that is, all its points have the same isotropy groups.

Symplectic Geometry · Mathematics 2020-10-19 Vicente Muñoz , Juan Angel Rojo

We derive an explicit expression for the star product reproducing the $\kappa$-Minkowski Lie algebra in any dimension $n$. The result is obtained by suitably reducing the Wick-Voros star product defined on $\mathbb{C}^{d}_\theta$ with…

Mathematical Physics · Physics 2015-10-27 Anna Pachol , Patrizia Vitale

In this article we propose a generalization of the 2-dimensional notions of convexity resp. being star-shaped to symplectic vector spaces. We call such curves symplectically convex resp. symplectically star-shaped. After presenting some…

Symplectic Geometry · Mathematics 2022-12-29 Peter Albers , Serge Tabachnikov

We relate the Bohr-Sommerfeld conditions established in microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian submanifold L, i.e. products preserving the…

Quantum Algebra · Mathematics 2007-11-19 Michael Carl

For arbitrary compact quantizable Kaehler manifolds it is shown how a natural formal deformation quantization (star product) can be obtained via Berezin-Toeplitz operators. Results on their semi-classical behaviour (their asymptotic…

Quantum Algebra · Mathematics 2007-05-23 Martin Schlichenmaier

We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold $M$. By combining differential geometry and analysis techniques, we establish the…

Analysis of PDEs · Mathematics 2025-07-16 Nicolas Martinez-Alba , Oscar Riaño

A study of symplectic actions of a finite group $G$ on smooth 4-manifolds is initiated. The central new idea is the use of $G$-equivariant Seiberg-Witten-Taubes theory in studying the structure of the fixed-point set of these symmetries.…

Geometric Topology · Mathematics 2007-09-12 Weimin Chen , Slawomir Kwasik

A semicontinuous semifinite trace is constructed on the C*-algebra generated by the finite propagation operators acting on the L^2-sections of a hermitian vector bundle on an amenable open manifold of bounded geometry. This trace is the…

Differential Geometry · Mathematics 2007-05-23 Daniele Guido , Tommaso Isola

Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show…

Mathematical Physics · Physics 2009-11-13 Paolo Aniello

This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local…

Discrete Mathematics · Computer Science 2014-07-14 Marc Hellmuth , Wilfried Imrich , Tomas Kupka