1995/05/31 by J. Donin · 14 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Boundary value problem #First class constraint #Homotopy and Cohomology in Algebraic Topology #Invertible matrix #Lie algebra #Mathematical analysis #Mathematics #Moment map #Poisson algebra #Poisson bracket #Poisson distribution #Poisson manifold #Pure mathematics #Quantization (signal processing) #Symplectic geometry #Uniqueness theorem for Poisson's equation #math.QA #q-alg
paper · pdf · doi:10.1006/aima.1997.1626
published in Advances in Mathematics 127(1), 73-93 (Elsevier BV) · Latex, 24 pp., essentially corrected version
arxiv created 1995/06/08 · openalex publication_date 1997/04/01 · arxiv updated 2011/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov's method we prove that any locally free nonsingular Poisson bracket can be quantized. In particular, it follows from this that all Poisson brackets on an arbitrary field of characteristic zero can be quantized. The well known theorem about the quantization of nondegenerate Poisson brackets on smooth manifolds follows from the main result of this paper as well.