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Related papers: Traces for star products on symplectic manifolds

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In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces which originally had been introduced by Chen. We explain the notion of a vector orbibundle and characterize the good sections of a…

Mathematical Physics · Physics 2007-05-23 Markus J. Pflaum

We give characterizations for the existence of traces for first order Sobolev spaces defined on regular trees.

Functional Analysis · Mathematics 2021-12-28 Pekka Koskela , Khanh Ngoc Nguyen , Zhuang Wang

We review our construction of star-products on Poisson manifolds and discuss some examples. In particular, we work out the relation with Fedosov's original construction in the symplectic case.

Quantum Algebra · Mathematics 2020-05-29 Alberto S. Cattaneo , Giovanni Felder , Lorenzo Tomassini

We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about…

Representation Theory · Mathematics 2024-03-27 Wen-Wei Li

The existence of nontrivial cup products or Massey products in the cohomology of a manifold leads to inequalities of systolic type, but in general such inequalities are not optimal (tight). Gromov proved an {optimal} systolic inequality for…

Differential Geometry · Mathematics 2024-07-08 Thomas G. Goodwillie , James J. Hebda , Mikhail G. Katz

A famous result of Jurgen Moser states that a symplectic form on a compact manifold cannot be deformed within its cohomology class to an inequivalent symplectic form. It is well known that this does not hold in general for noncompact…

Symplectic Geometry · Mathematics 2018-01-30 Sean Curry , Álvaro Pelayo , Xiudi Tang

In this letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of Wick type on every K\"ahler manifold by a…

q-alg · Mathematics 2008-02-03 M. Bordemann , S. Waldmann

We derive global curvature estimates for closed, strictly star-shaped $(n-2)$-convex hypersurfaces in warped product manifolds, which satisfy the prescribed $(n-2)$-curvature equation with a general right-hand side. The proof can be readily…

Analysis of PDEs · Mathematics 2024-11-18 Bin Wang

In this article we relate the construction of Ricci type symplectic connections by reduction to the construction of star product by reduction yielding rather explicit descriptions for the star product on the reduced space.

Quantum Algebra · Mathematics 2007-10-09 Michel Cahen , Simone Gutt , Stefan Waldmann

We introduce the notion of asymptotically finitely generated contact structures, which states essentially that the Symplectic Homology in a certain degree of any filling of such contact manifolds is uniformly generated by only finitely many…

Symplectic Geometry · Mathematics 2020-07-20 Alexander Fauck

Given a locally convex vector space with a topology induced by Hilbert seminorms and a continuous bilinear form on it we construct a topology on its symmetric algebra such that the usual star product of exponential type becomes continuous.…

Quantum Algebra · Mathematics 2021-08-20 Matthias Schötz , Stefan Waldmann

We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local…

Geometric Topology · Mathematics 2010-06-03 P. Christopher Staecker

We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the…

Differential Geometry · Mathematics 2016-01-15 Jørgen Ellegaard Andersen , Paolo Masulli , Florian Schaetz

For every symmetrically normed ideal $\mathcal{E}$ of compact operators, we give a criterion for the existence of a continuous singular trace on $\mathcal{E}$. We also give a criterion for the existence of a continuous singular trace on…

Operator Algebras · Mathematics 2011-08-15 F. Sukochev , D. Zanin

The purpose of this short note is to establish an explicit equivalence between the two star products $\star$ and $\star_{\log}$ on the symmetric algebra $\mathrm S(\mathfrak g)$ of a finite-dimensional Lie algebra $\mathfrak g$ over a field…

Quantum Algebra · Mathematics 2012-09-14 Carlo A. Rossi

We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star…

Quantum Algebra · Mathematics 2017-11-21 Francesco D'Andrea , Thomas Weber

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…

High Energy Physics - Theory · Physics 2010-05-13 Shannon McCurdy , Bruno Zumino

Product Lagrangian tori in standard symplectic space $R^{2n}$ were classified up to symplectomorphism in [Che96]. We extend this classification to tame symplectically aspherical symplectic manifolds. We show by examples that the asphericity…

Symplectic Geometry · Mathematics 2015-02-03 Yuri Chekanov , Felix Schlenk

We give a description of traces on C(X)\rtimes G in terms of measurable fields of traces on the C*-algebras of the stabilizers of the action of G on X.

Operator Algebras · Mathematics 2010-10-05 Sergey Neshveyev

We show that there is an obstruction to the existence of a star product defined by Kontsevich graphs without directed cycles.

Quantum Algebra · Mathematics 2015-02-23 Thomas Willwacher