Lectures on integrability of Lie brackets
Lectures on integrability of Lie brackets
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李括号可积性讲座
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
M. Crainic
中科院分区：
文献类型：
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作者：
R. Fernandes;M. Crainic
这些笔记由五个讲座组成。在第一堂课中，我们介绍李群胚和它们的无穷小版本。在第二堂课中，我们介绍了李代数胚的抽象概念，并解释了有多少微分几何的概念可以用这种语言来描述。第1讲和第2讲应该可以帮助你熟悉李群胚和李代数胚的语言。第3课和第4课涉及可积性问题的各个方面。这两堂课是本课程的核心内容，并包含对可积性障碍的详细描述。在第五课中，我们将考虑与泊松几何相关的可积性方面作为例子。在
These notes are made up of five lectures. In Lecture 1, we introduce Lie groupoids and their infinitesimal versions. In Lecture 2, we introduce the abstract notion of a Lie algebroid and explain how many notions of differential geometry can be described in this language. Lectures 1 and 2 should help you in becoming familiar with the language of Lie groupoids and Lie algebroids. Lectures 3 and 4 are concerned with the various aspects of the integrability problem. These two lectures form the core material of this course and contain a detailed description of the integrability obstructions. In Lecture 5 we consider, as an example, aspects of integrability related to Poisson geometry. At