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arXiv · 0707.2867

Quadratic Deformations of Lie-Poisson Structures

Qian Lin·Zhangju Liu·Yunhe Sheng
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Abstract

In this letter, first we give a decomposition for any Lie-Poisson structure $π_g$ associated to the modular vector. In particular, $π_g$ 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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Qian Lin, Zhangju Liu, Yunhe Sheng. 2010-07-14. Quadratic Deformations of Lie-Poisson Structures. https://doi.org/10.1007/s11005-008-0221-3

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