The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures

Details The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures

1996-05-09

arxiv.org/abs/hep-th/9605067v2

J.Phys.A29:7993-8010,1996

Physics

High Energy Physics

High Energy Physics - Theory

29 pages. Plain TeX. Phyzzx needed. An example and some references added. To appear in J. Phys. A

Scientific paper

10.1088/0305-4470/29/24/023

Newly introduced generalized Poisson structures based on suitable skew-symmetric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras.

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