Foliated groupoids and infinitesimal ideal systems
Foliated groupoids and infinitesimal ideal systems
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DOI：
10.1016/j.indag.2014.07.009
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发表时间：
2014-10
期刊：
影响因子：
--
通讯作者：
M. J. Lean;Cristian Ortiz
中科院分区：
文献类型：
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作者：
M. J. Lean;Cristian Ortiz
这项工作的主要目的是在李代数体中引入理想的一个自然概念，即“无穷小理想系统”。李代数中的理想和与切丛的对合子丛相关的Bott联络是特例。这些对象的定义是由李群胚上的对合乘法分布的无穷小刻画而来的。在李群的情况下，这样的分布对应于理想。给出了无穷小理想系统的几个例子，并且在适当的正则性条件下，证明了由无限小理想系统构成的李代数体的商是李代数体。
The main goal of this work is to introduce a natural notion of ideal in a Lie algebroid, the “infinitesimal ideal systems”. Ideals in Lie algebras and the Bott connection associated to involutive subbundles of tangent bundles are special cases. The definition of these objects is motivated by the infinitesimal description of involutive multiplicative distributions on Lie groupoids. In the Lie group case, such distributions correspond to ideals. Several examples of infinitesimal ideal systems are presented, and (under suitable regularity conditions) the quotient of a Lie algebroid by an infinitesimal ideal system is shown to be a Lie algebroid.