Integration of twisted Dirac brackets
Integration of twisted Dirac brackets
复制标题
扭曲狄拉克支架的整合
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Chenchang Zhu
中科院分区：
文献类型：
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作者：
H. Bursztyn;M. Crainic;A. Weinstein;Chenchang Zhu
给定流形M上的一个李群胚G，我们证明了G上相对于闭的3-形式Phi相对闭的乘法2-形式对应于从G的李代数体到T*M的映射满足一个代数条件和一个关于Phi-扭曲Courant括号的微分条件.作为特例，这种对应关系描述了与Phi扭曲的狄拉克结构相关联的全局对象。作为应用，我们将我们的结果与等变上同调和分层理论联系起来，给出了拟哈密顿空间和群值动量映射的新刻画。
Given a Lie groupoid G over a manifold M, we show that multiplicative 2-forms on G relatively closed with respect to a closed 3-form phi on M correspond to maps from the Lie algebroid of G into T* M satisfying an algebraic condition and a differential condition with respect to the phi-twisted Courant bracket. This correspondence describes, as a special case, the global objects associated to phi-twisted Dirac structures. As applications, we relate our results to equivariant cohomology and foliation theory, and we give a new description of quasi-Hamiltonian spaces and group-valued momentum maps.