积分无穷小（超）作用量
Integrating infinitesimal (super) actions
摘要：
本文将Richard Palais的一些结果推广到李超群和李超代数的情况。更精确地说，令$G$是一个李超群，$\mathfrak g$是它的李超代数，令$ρ$是$M$上的$\mathfrak g$的无穷小作用（表示）。我们将证明在$M$上总是存在$G$的局部（光滑左）作用，使得$ρ$是将$M$上的基本向量场关联到代数元素的映射（我们将说该作用对$ρ$进行积分）。证明了若$ρ$是单价的，则存在唯一的$G$对积分为$ρ$的$M$的极大局部作用.最后我们证明，如果$G$是单连通的并且所有（光滑、偶数）向量场$ρ(X)$都是完整的，那么存在$G$对$M$积分$ρ$的全局（光滑左）作用。省略所有对超级设置的引用将使我们的校样变成宫殿的变体。
英文摘要：
In this paper we generalize some results of Richard Palais to the case of Lie supergroups and Lie superalgebras. More precisely, let $G$ be a Lie supergroup, $\mathfrak g$ its Lie superalgebra and let $ρ$ be an infinitesimal action (a representation) of $\mathfrak g$ on a supermanifold $M$. We will show that there always exists a local (smooth left) action of $G$ on $M$ such that $ρ$ is the map that associates the fundamental vector field on $M$ to an algebra element (we will say that the action integrates $ρ$). We also show that if $ρ$ is univalent, then there exists a unique maximal local action of $G$ on $M$ integrating $ρ$. And finally we show that if $G$ is simply connected and all (smooth, even) vector fields $ρ(X)$ are complete then there exists a global (smooth left) action of $G$ on $M$ integrating $ρ$. Omitting all references to the super setting will turn our proofs into variations of those of Palais.
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