1998/02/06 by Byung-Jay Kahng, Kahng, Byung-Jay
Mathematics · #22D25 #46L87 (Primary) 58F05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.FA #math.OA #math.QA #msc:22D25 #msc:46L87 #msc:58F05
paper · pdf · doi:10.48550/arxiv.math/9802034
AMS-LaTeX v1.2, 26 pages, to appear in International Journal of Mathematics
arxiv created 1998/02/06 · openalex publication_date 1998/02/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain non-linear Poisson brackets which are ``cocycle perturbations'' of the linear Poisson bracket. We show that these special Poisson brackets are equivalent to Poisson brackets of central extension type, which resemble the central extensions of an ordinary Lie bracket via Lie algebra cocycles. We are able to formulate (strict) deformation quantizations of these Poisson brackets by means of twisted group C*-algebras. We also indicate that these deformation quantizations can be used to construct some specific non-compact quantum groups.