Globalizations of infinitesimal actions on supermanifolds

Abstract

Let $\mathcal{G}$ be a Lie supergroup with Lie superalgebra $\mathfrak{g}$, $\mathcal{M}$ a supermanifold and $\mathrm{Vec}(\mathcal{M})$ the set of vector fields on $\mathcal{M}$. Let $\lambda :\mathfrak{g}\to \mathrm{Vec}(\mathcal{M})$ be an infinitesimal action, i.e. a homomorphism of Lie superalgebras. We show the existence of a local $\mathcal{G}$-action on $\mathcal{M}$ inducing the infinitesimal action $\lambda$ and find necessary and sufficient conditions for the existence of a globalization in the sense of Palais.

arXiv comment30 pages