LOCAL FORMULAS FOR MULTIPLICATIVE FORMS
LOCAL FORMULAS FOR MULTIPLICATIVE FORMS
复制标题
乘法形式的局部公式
DOI：
10.1007/s00031-020-09607-y
复制
发表时间：
2018
影响因子：
0.7
通讯作者：
M. A. Salazar
中科院分区：
文献类型：
--
作者：
A. Cabrera;I. Mărcuţ;M. A. Salazar
我们提供了根据无穷小数据在局部李群形上积分乘法形式的显式公式。结合我们之前的工作[8]，该工作构造了李代数体的局部李群群，这些公式产生了几个无限小定义的几何结构的具体积分。特别是，我们分别通过局域辛、辛-Nijenhuis、前辛和接触群形获得泊松、Nijenhuis-Poisson、Dirac 和 Jacobi 结构的局部积分和非简并实现。
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.