The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures
High Energy Physics - Theory
2008-11-26 v2 dg-ga
Differential Geometry
Quantum Algebra
q-alg
Abstract
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.
Keywords
Cite
@article{arxiv.hep-th/9605067,
title = {The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures},
author = {J. A. de Azcarraga and A. M. Perelomov and J. C. Perez Bueno},
journal= {arXiv preprint arXiv:hep-th/9605067},
year = {2008}
}
Comments
29 pages. Plain TeX. Phyzzx needed. An example and some references added. To appear in J. Phys. A