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| arXiv:0707.2867 |
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Title: Quadratic Deformations of Lie-Poisson Structures
Authors: Lin Qian, Liu Zhangju, Sheng Yunhe
Categories: math.DG Differential Geometry (physics.math-ph Mathematical Physics)
Comments: 14 pages, no figure
Journal reference: Lett. Math. Phys. (2008) 83:217-229
Abstract: 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.
Owner: Sheng Yunhe
Version 1: Thu, 19 Jul 2007 10:10:47 GMT
Version 2: Thu, 16 Aug 2007 15:04:51 GMT
Version 3: Tue, 25 Mar 2008 18:11:10 GMT
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