AI 中文总结
该研究引入导出李n-群胚及其平移辛结构，定义平移拉格朗日结构并证明其合成条件，框架包含多种临界值约化过程，如经典哈密顿约化等，为相关研究提供新视角与方法。
AI 中文摘要
这项工作的主要目标是引入导出李n-群胚及其平移辛结构。我们进一步定义了平移拉格朗日结构，并证明在适当条件下它们的合成是定义良好的。作为应用，我们表明我们的框架包含几个临界值处的约化过程，包括经典哈密顿约化、群值矩映射、泊松李群值矩映射以及适当辛群胚的三上-温斯坦约化。
英文摘要
The main goal of this work is to introduce derived Lie n-groupoids and their shifted symplectic structures. We further define shifted lagrangian structures and prove that their composition is well defined under suitable conditions. As an application, we show that our framework incorporates several reduction procedures at critical values, including: classical Hamiltonian reduction, group valued moment maps, Poisson Lie group valued moment maps and Mikami-Weinstein for proper symplectic groupoids.
Comments71 pages
