Flat left-invariant connections adapted to the automorphism structure of a Lie group
Flat left-invariant connections adapted to the automorphism structure of a Lie group
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DOI：
10.4310/jdg/1214436223
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发表时间：
1981
影响因子：
2.5
通讯作者：
Alberto Medina Perea
中科院分区：
文献类型：
--
作者：
Alberto Medina Perea
假设 A' 是李代数 K 的李群，并且 Aut(^)（分别为 \nt(K)）是代数 K 的自同构群（分别为内部自同构）。K 的局部自同构（分别为局部内部自同构）结构是通过扩展到 Aut(K)（分别为 lni(K)）而获得的框架的主纤维丛 K 的左不变平行性。它的纤维是唯一的，直到 Ks 框架丛 R(K) 中的右平移。在本文中，我们开始研究适应上面定义的结构的左不变局部平坦连接。
Suppose that A' is a Lie group with Lie algebra K, and further that Aut(^) (respectively \nt(K)) is the group of automorphisms (resp. interior automorphisms) of the algebra K. The local automorphism (resp. local interior automorphism) structure of K is the principal fiber bundle of frames obtained by the extension to Aut(K) (resp. lni(K)) of a left-invariant parallelism of K. Its fibers are unique, up to a right translation in Ks frame bundle R(K). In this article we commence a study of left-invariant locally flat connections adapted to the structures defined above.