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- W1756982800 abstract "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 $rho$ 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 $rho$ is the map that associates the fundamental vector field on $M$ to an algebra element (we will say that the action integrates $rho$). We also show that if $rho$ is univalent, then there exists a unique maximal local action of $G$ on $M$ integrating $rho$. And finally we show that if $G$ is simply connected and all (smooth, even) vector fields $rho(X)$ are complete then there exists a global (smooth left) action of $G$ on $M$ integrating $rho$. Omitting all references to the super setting will turn our proofs into variations of those of Palais." @default.
- W1756982800 created "2016-06-24" @default.
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- W1756982800 date "2013-02-12" @default.
- W1756982800 modified "2023-09-27" @default.
- W1756982800 title "Integrating infinitesimal (super) actions" @default.
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