Linear Poisson structures on R4

2007/07/31 by Yunhe Sheng · 1 citation
Mathematics · Medicine · Physics and Astronomy · #Advanced Topics in Algebra #Affine transformation #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Lie group #Mathematics #Medicine #Philosophy #Poisson distribution #Poisson regression #Pure mathematics #Scroll #Statistics #Unimodular matrix #math-ph #math.DG #math.MP

paper · pdf · doi:10.1016/j.geomphys.2007.08.008

published as J. Geom. Phys. 57 (2007), 2398-2410 · 14 pages, no figure

openalex publication_date 2007/08/23 · arxiv created 2010/07/14 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 R³ are totally classified.

Citations

• The modular automorphism group of a Poisson manifold

Cited by

• Quadratic Deformations of Lie–Poisson Structures