1996/12/31 by J. A. de Azcarraga, J. A. de Azcárraga, José Izquierdo +4 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Bracket #Covariance and contravariance of vectors #Degenerate energy levels #Lie algebra #Lie superalgebra #Mathematics #Nonlinear Waves and Solitons #Physics #Poisson bracket #Poisson distribution #Pure mathematics #Supermanifold #dg-ga #hep-th #math.DG #math.QA #q-alg
paper · pdf · doi:10.1063/1.532065
published as J.Math.Phys. 38 (1997) 3735-3749 · Latex/RevTeX file. 25 pages. Minor corrections and references added. To appear in J. Math. Phys
arxiv created 1997/04/05 · openalex publication_date 1997/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The super or Z2-graded Schouten–Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors Λ of even order. The corresponding super “Jacobi identities” are expressed by stating that these tensors have a zero super Schouten–Nijenhuis bracket with themselves [Λ,Λ]=0. As a particular case, we provide the linear generalized super-Poisson structures which can be constructed on the dual spaces of simple superalgebras with a non-degenerate Killing metric. The su(3,1) superalgebra is given as a representative example.