Integration of Vector Fields on Smooth and Holomorphic Supermanifolds

We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on complex supermanifolds. Furthermore we discuss local actions associated to super vector fields, and give several examples and applications, as, e.g., the construction of an exponential morphism for an arbitrary finite-dimensional Lie supergroup.

2010 Mathematics Subject Classification: Primary 58A50, 37C10; Secondary 57S20, 32C11

Keywords and Phrases: Supermanifolds; Vector fields; Flows; Group actions

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