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arXiv · hep-th/9612186

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

J. A. de Azcarraga·J. M. Izquierdo·A. M. Perelomov·J. C. Perez Bueno
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Abstract

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 Λof even order. The corresponding super `Jacobi identities' are expressed by stating that these tensors have 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 generic example.

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J. A. de Azcarraga, J. M. Izquierdo, A. M. Perelomov, J. C. Perez Bueno. 1997-04-05. The Z_2-graded Schouten-Nijenhuis bracket and generalized super-Poisson structures. https://doi.org/10.1063/1.532065

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