论文标题
非连接的谎言组，扭曲的模棱两可的捆绑包和覆盖物
Non-connected Lie groups, twisted equivariant bundles and coverings
论文作者
论文摘要
让$γ$成为一个有限的集团，该集团在谎言组$ g $上。我们考虑一类组扩展名$ 1 \ to g \ to \ hat {g} \toγ\至1 $由此操作定义的$ 2 $ -COCYCLE $ 2 $ cOCYCLE $γ$，其价值为$ G $。我们建立并研究了$ \ hat {g} $ - 在歧管上的捆绑和扭曲的$γ$ equivariant捆绑包，结构组$ g $在合适的galois $γ$上覆盖了歧管。我们还用非亚伯式的共同体来描述这种对应关系。我们的结果尤其适用于紧凑或还原的复杂谎言组$ \ hat {g} $，因为这样的组始终对上述扩展是同构的，其中$ g $是身份的连接组件，$γ$是$ \ hat {g} $的连接组件的组。
Let $Γ$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to Γ\to 1$ defined by this action and a $2$-cocycle of $Γ$ with values in the centre of $G$. We establish and study a correspondence between $\hat{G}$-bundles on a manifold and twisted $Γ$-equivariant bundles with structure group $G$ on a suitable Galois $Γ$-covering of the manifold. We also describe this correspondence in terms of non-abelian cohomology. Our results apply, in particular, to the case of a compact or reductive complex Lie group $\hat{G}$, since such a group is always isomorphic to an extension as above, where $G$ is the connected component of the identity and $Γ$ is the group of connected components of $\hat{G}$.
