结构李群胚的覆盖与作用I
Coverings and Actions of Structured Lie Groupoids I
摘要：
本文研究了李群-群胚作为一类结构李群胚的覆盖和作用。首先，我们定义了李群-群胚在某些李群上的作用以及李群-群胚的光滑覆盖。然后，我们证明了李群-群胚在李群上的光滑作用范畴与李群-群胚的光滑覆盖范畴的等价性。进一步证明了如何从李群-群胚得到覆盖李群-群胚和李群-群胚的光滑覆盖射的定理。
英文摘要：
In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids. Later, we show the equivalence of the category of smooth actions of Lie group-groupoids on Lie groups and the category of smooth cov- erings of Lie group-groupoids. Further, we prove a theorem which denotes how is obtained a covering Lie group-groupoid and a smooth covering morphism of Lie group-groupoids from a Lie group-groupoid.
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