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Journal of Lie Theory 24 (2014), No. 3, 809--847
Copyright Heldermann Verlag 2014

Globalizations of Infinitesimal Actions on Supermanifolds

Hannah Bergner
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany

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

Keywords: Supermanifold, Lie supergroup, vector field, distribution, infinitesimal action, local action, globalization.

MSC: 58A50, 17B66; 57S20, 32C11

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