Quantization of Poisson families and of twisted Poisson structures

2002/05/28 by Pavol Ševera, Pavol Severa, Severa, Pavol · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math.QA #math.SG

paper · pdf · doi:10.48550/arxiv.math/0205294

7 pages, 3 figures

arxiv created 2002/05/28 · openalex publication_date 2002/05/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures given by a Maurer-Cartan equation; they are easily quantized using Kontsevich's Formality theorem.

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• BV Quantization of Topological Open Membranes

Related

• Poisson geometry with a 3-form background
• Kontsevich's deformation quantization: from Dirac to multiple zeta values
• Lectures on Deformation quantization of Poisson manifolds
• Commutative Poisson algebras from deformations of noncommutative algebras
• Deformation Quantization of Certain Non-linear Poisson Structures