Linear Poisson structures on R^4

Abstract

We classify all of the 4-dimensional linear Poisson structures of which the corresponding Lie algebras can be considered as the extension by a derivation of 3-dimensional unimodular Lie algebras. The affine Poisson structures on R^3 are totally classified.

14 pages, no figure

Cited by in corpus (4)

• Representations of hom-Lie algebras
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• On Computational Poisson Geometry II: Numerical Methods
• Quadratic Deformations of Lie-Poisson Structures