相配群胚上的诱导联络(英文)  

Induced Connections of Associated Groupoids

作　　者：袁丽霞[1] 王宝勤[1] 

机构地区：[1]新疆师范大学数理信息学院,乌鲁木齐新疆830054

出　　处：《数学进展》2008年第5期617-624,共8页Advances in Mathematics（China）

基　　金：NSFC(No.10472100).

摘　　要：本文引入了相配群胚和相配主丛的概念,它们是一对具有相同传递函数的局部平凡李群胚(Г→_→P,α,β)和主丛(B,P,π,G).我们首先考察了相配群胚Г的内子群胚GГ的局部平凡化,利用这个局部平凡化证明了在B和GГ之间自然存在着一个丛同构.通过这个丛同构以及B的联络日逐步得到了H在GГ和Г上的诱导联络,进而定义了Г上分别以α,β为投影的左联络和右联络,这两个联络都是在Г上整体有定义的,与以往李群胚上的联络只是定义在李代数胚上不同.In this paper, the new concepts of associated groupoids and associated principal bundle be introduced which are a pair of a locally trivial Lie groupoids （Г→_→P,α,β） and a principal bundle （B,P,π,G） with the same transition function. At first, ＂the locally trivializations of the inner aubgroupoids GF of F is considered, then, by using the locally trivializations, it is proved that there is a natural bundle isomorphism between B and GF. By this bundle isomorphism and the connections H of B, the induced connections on GF and F are obtained gradually. Furthermore, we constructed a left connections and a right connections of F which are respectively regard α, β as their projections. The two connections are defined on the whole Г. It is differs from before that the connections of a Lie groupoids only be defined on its Lie algebroids.

关 键 词：相配群胚 诱导联络 联络 

分 类 号：O186[理学—数学]