Hochschild Cohomology and Deformation Quantization of Affine Toric Varieties

2017/06/02 by Matej Filip, Filip, Matej
Mathematics · #Advanced Algebra and Geometry #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.1706.00580

openalex publication_date 2017/06/02 · arxiv created 2018/03/20 · arxiv updated 2018/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an affine toric variety Spec(A), we give a convex geometric description of the Hodge decomposition of its Hochschild cohomology. Under certain assumptions we compute the dimensions of the Hodge summands T¹_(i)(A), generalizing the existing results about the Andre-Quillen cohomology group T¹₍₁₎(A). We prove that every Poisson structure on a possibly singular affine toric variety can be quantized in the sense of deformation quantization.

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