The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures

de Azcarraga, J. A.; Perelomov, A. M.; Bueno, J. C. Perez

The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures

Authors

de Azcarraga, J. A.

Perelomov, A. M.

Bueno, J. C. Perez

Description

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