Quasi-Poisson Manifolds
Quasi-Poisson Manifolds
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DOI：
10.4153/cjm-2002-001-5
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发表时间：
2000-06
期刊：
影响因子：
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通讯作者：
Anton Alekseev;Y. Kosmann-Schwarzbach;E. Meinrenken
中科院分区：
文献类型：
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作者：
Anton Alekseev;Y. Kosmann-Schwarzbach;E. Meinrenken
拟Poisson流形是具有不变双向量场的$G$-流形，其Schouten括号是由与不变内积相关的不变元生成的三向量场。我们引入了这类流形的融合的概念，并将拟Poisson流形与前面引入的具有群值矩映射的拟哈密顿流形联系起来。
Abstract A quasi-Poisson manifold is a $G$ -manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in ${{\Lambda }^{3}}\mathfrak{g}$ associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.