Quasi-Poisson structures and integrable systems related to the moduli space of flat connections on a punctured Riemann sphere

JOURNAL OF GEOMETRY AND PHYSICS

卷:57

Article

Le Blanc, Ariane

关键词: (quasi-)Poisson manifolds;    integrable systems;    Poisson reduction;   

DOI  :  10.1016/j.geomphys.2007.01.006

来源: Elsevier

【 摘 要 】

In order to construct an integrable system on the moduli space Hom(pi(1) (S), G)/G of a punctured sphere S, we establish a morphism between two interesting quasi-Poisson G-manifolds, G(n) and a subspace g(n) of the loop algebra of g. In particular, we prove a useful result about reduction in the quasi-Poisson context and we describe the construction of a quasi-Poisson structure coming from a Lie algebra splitting. (c) 2007 Elsevier B.V. All rights reserved.

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