Twisted Deformation Quantization of Algebraic Varieties (Survey)

2008/01/21 by Amnon Yekutieli, Yekutieli, Amnon
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AG #math.QA

paper · pdf · doi:10.48550/arxiv.0801.3233

Lecture notes made into a survey article. 19 pages. To appear in Cont. Math. (Goodearl Conference Proceedings)

openalex publication_date 2008/01/21 · arxiv created 2011/07/27 · arxiv updated 2011/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that there is a twisted quantization map from twisted Poisson deformations to twisted associative deformations, which is canonical and bijective on equivalence classes.

Related

• Twisted Deformation Quantization of Algebraic Varieties
• Deformation Quantization in Algebraic Geometry
• Deformations of Affine Varieties and the Deligne Crossed Groupoid
• On the deformation quantization of affine algebraic varieties
• Derived Algebraic Geometry and Deformation Quantization