A covariant Poisson deformation quantization with separation of variables up to the third order

2002/06/25 by Alexander Karabegov, Karabegov, Alexander
Mathematics · #53C55 #53D55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:53C55 #msc:53D55

paper · pdf · doi:10.48550/arxiv.math/0206271

9 pages, minor typos corrected

openalex publication_date 2002/06/25 · arxiv created 2002/06/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a simple formula for the operator C₃ of the standard deformation quantization with separation of variables on a Kähler manifold M. Unlike C₁ and C₂, this operator can not be expressed in terms of the Kähler-Poisson tensor on M. We modify C₃ to obtain a covariant deformation quantization with separation of variables up to the third order which is expressed in terms of the Poisson tensor on M and thus can be defined on an arbitrary complex manifold endowed with a Poisson bivector field of type (1,1).

Related

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