Polynomial poly-vector fields
Differential Geometry
2011-05-23 v4 Mathematical Physics
math.MP
Abstract
In this text we give a decomposition result on polynomial poly-vector fields generalizing a result on the decomposition of homogeneous Poisson structures. We discuss consequences of this decomposition result in particular for low dimensions and low degrees. We provide the tools to calculate simple cubic Poisson structures in dimension three and quadratic Poisson structures in dimension four. Our decomposition result has a nice effect on the relation between Poisson structures and Jacobi structures.
Cite
@article{arxiv.math/0409157,
title = {Polynomial poly-vector fields},
author = {Frank Klinker},
journal= {arXiv preprint arXiv:math/0409157},
year = {2011}
}
Comments
20 pages. v4: sections rearranged and formulations clarified