We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the local Lie groupoid of a Lie algebroid, these formulas produce concrete integrations of several geometric stuctures defined infinitesimally. In particular, we obtain local integrations and non-degenerate realizations of Poisson, Nijenhuis–Poisson, Dirac, and Jacobi structures by local symplectic, symplectic-Nijenhuis, presymplectic, and contact groupoids, respectively.

中文翻译：

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乘法形式的局部公式

我们提供了无穷小数据，用于在局部李群群上整合乘法形式的显式公式。结合我们先前的工作[8]，该工作构造了一个李代数的局部李群群，这些公式产生了无穷定义的几种几何结构的具体积分。特别是，我们分别通过局部辛，辛辛-尼延惠斯，辛折前和接触群形来获得Poisson，Nijenhuis-Poisson，Dirac和Jacobi结构的局部积分和非简并实现。