The Z_2-graded Schouten-Nijenhuis bracket and generalized super-Poisson structures

Details The Z_2-graded Schouten-Nijenhuis bracket and generalized super-Poisson structures The Z_2-graded Schouten-Nijenhuis bracket and generalized super-Poisson structures

1996-12-18

arxiv.org/abs/hep-th/9612186v2

J.Math.Phys. 38 (1997) 3735-3749

Physics

High Energy Physics

High Energy Physics - Theory

Latex/RevTeX file. 25 pages. Minor corrections and references added. To appear in J. Math. Phys

Scientific paper

10.1063/1.532065

The super or Z_2-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 \Lambda of even order. The corresponding super `Jacobi identities' are expressed by stating that these tensors have zero super Schouten-Nijenhuis bracket with themselves [\Lambda,\Lambda]=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 generic example.

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