Quadratic Deformations of Lie-Poisson Structures

Details Quadratic Deformations of Lie-Poisson Structures Quadratic Deformations of Lie-Poisson Structures

2007-07-19

arxiv.org/abs/0707.2867v4

Lett. Math. Phys. (2008) 83:217-229

Mathematics

Differential Geometry

14 pages, no figure

Scientific paper

In this letter, first we give a decomposition for any Lie-Poisson structure
$\pi_g$ associated to the modular vector. In particular, $\pi_g$ splits into
two compatible Lie-Poisson structures if $dim{g} \leq 3$. As an application, we
classified quadratic deformations of Lie-Poisson structures on $\mathbb R^3$ up
to linear diffeomorphisms.

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