Abstract
In this chapter we consider weight homogeneous Poisson structures, the simplest of which (homogeneous Poisson structures of degree 0 or 1) have been considered in the previous chapters. Other distinguished classes of weight homogeneous Poisson structures, considered in this chapter, are quadratic Poisson structures (for which a partial classification is given, with the help of the modular vector field), rank two Poisson structures arizing from weight homogeneous Nambu–Poisson structures and the transverse Poisson structures to adjoint orbits in a semi-simple Lie algebra.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Laurent-Gengoux, C., Pichereau, A., Vanhaecke, P. (2013). Higher Degree Poisson Structures. In: Poisson Structures. Grundlehren der mathematischen Wissenschaften, vol 347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31090-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-31090-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31089-8
Online ISBN: 978-3-642-31090-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)