2009/08/28 by Gilles Halbout, Xiang Tang, Halbout, Gilles +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.DG #math.QA
paper · pdf · doi:10.48550/arxiv.0908.4301
24 pages
openalex publication_date 2009/08/28 · arxiv created 2010/09/30 · arxiv updated 2010/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X,ω) be a symplectic orbifold which is locally like the quotient of a ℤ2 action on \realsn. Let A((ℏ))X be a deformation quantization of X constructed via the standard Fedosov method with characteristic class being ω. In this paper, we construct a universal deformation of the algebra A((ℏ))X parametrized by codimension 2 components of the associated inertia orbifold \widetildeX. This partially confirms a conjecture of Dolgushev and Etingof in the case of ℤ2 orbifolds. To do so, we generalize the interpretation of Moyal star-product as a composition of symbol of pseudodifferential operators in the case where partial derivatives are replaced with Dunkl operators. The star-products we obtain can be seen as globalizations of symplectic reflection algebras.