Integrable lifts for transitive Lie algebroids
Integrable lifts for transitive Lie algebroids
复制标题
传递李代数体的可积提升
DOI：
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发表时间：
2017
影响因子：
0.6
通讯作者：
P. Antonini
中科院分区：
文献类型：
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作者：
Iakovos Androulidakis;P. Antonini
受 Molino 工作的启发，我们证明了传递李代数体的可积性障碍可以通过添加额外的维度来消失。特别是，我们证明了不可积传递和阿贝尔李代数体的韦恩斯坦群群是有限维李群群的商。给出了两个这样的构造：首先，解释了 Almeida 和 Molino 给出的可积性的反例，我们看到它可以推广到当基本流形简单连接时“Almeida-Molino”可积升力的构造。另一方面，我们注意到经典的德拉姆同构提供了一个通用的可积代数体。使用它，我们为任何给定的传递阿贝尔李代数体构建了“de Rham”可积升力。
Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid is the quotient of a finite-dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an “Almeida–Molino” integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a “de Rham” integrable lift for any given transitive Abelian Lie algebroid.
DOI：
10.1007/s00029-017-0319-5
发表时间：
2017
期刊：
Selecta Mathematica
影响因子：
--
作者：
I. Androulidakis;M. Zambon
通讯作者：
M. Zambon