CAJ | 학술논문

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H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.
본문인입료상배군배화상배주총적개념,타문시일대구유상동전체함수적국부평범리군배(Г(→→)P,α,β)화주총(B,P,π,G).아문수선고찰료상배군배Г적내자군배GГ적국부평범화,이용저개국부평범화증명료재B화GГ지간자연존재착일개총동구.통과저개총동구이급B적련락H축보득도료H재GГ화Г상적유도련락,진이정의료Г상분별이α,β위투영적좌련락화우련락,저량개련락도시재Г상정체유정의적,여이왕리군배상적련락지시정의재리대수배상불동.
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(F (→→)P,α,β)and a principal bundle(B,P,π,G)with the same transition function.At first,the locally trivializations of the inner subgroupoids 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 GГ and Г are obtained gradually.Furthermore,we constructed a left connections and a right connections of Г 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.