李代数胚的和乐群胚
On the holonomy of Lie algebroids
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中文总结 AI 辅助
本文引入李代数胚的和乐群胚，推广叶状结构和乐群胚与李代数伴随表示，证明其纵向光滑性并计算其李代数胚，利用流乘积构造其群胚结构，为Weinstein群胚提供新定义方式。
中文摘要 AI 辅助
我们引入了李代数胚的和乐群胚，该构造推广了叶状结构的和乐群胚以及李代数的伴随表示。我们证明所得群胚是纵向光滑的，并计算了其李代数胚。当和乐群胚的李代数胚与给定李代数胚一致时，该和乐群胚是典范的终端积分：每个源连通积分都存在唯一的态射映射到它，且无穷小层面诱导恒等映射。为在和乐群胚上构造群胚结构，我们利用李代数胚依赖时间的截面的“流乘积”概念，这为定义Weinstein群胚的群胚结构提供了另一种方式。
英文摘要
We introduce a holonomy groupoid for Lie algebroids. This construction generalizes both the holonomy groupoid of a foliation and the adjoint representation of a Lie algebra. We prove that the resulting groupoid is longitudinally smooth and compute its Lie algebroid. When the algebroid of the holonomy groupoid coincides with the given Lie algebroid, the holonomy groupoid is the canonical terminal integration: every source-connected integration admits a unique morphism into it inducing the identity infinitesimally. To construct the groupoid structure on the holonomy groupoid, we utilize the notion of the "flow product" of time-dependent sections of a Lie algebroid. This provides an alternative way to define the groupoid structure for the Weinstein groupoid.
