1997/07/02 by J. C. Perez Bueno, J C Pérez Bueno
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Cohomology #Generalization #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Poisson bracket #Poisson distribution #Simple (philosophy) #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0305-4470/30/18/024
published as J.Phys.A30:6509-6515,1997 · Latex2e file. 11 pages. To appear in J. Phys. A
arxiv created 1997/07/02 · openalex publication_date 1997/09/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a particular case, the recently introduced generalized Poisson structures. The linear case on simple group manifolds is also studied and non-trivial examples (different from those coming from generalized Poisson structures) of this new construction are found by using the cohomology ring of the given group.