2009/12/10 by Yuri A. Kordyukov, Kordyukov, Yuri A.
Mathematics · Physics and Astronomy · #37J05 #53C12 (Secondary) #58B34 (Primary) #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #math.DG #math.DS #msc:37J05 #msc:53C12 #msc:58B34
paper · pdf · doi:10.48550/arxiv.0912.1923
13 pages
arxiv created 2009/12/10 · openalex publication_date 2009/12/10 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
First, we review the notion of a Poisson structure on a noncommutative algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a noncommutative algebra associated with a transversely symplectic foliation and construct a class of Hamiltonian vector fields associated with this Poisson structure.