Abstract
Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of innite-dimension al Lie groups how to construct a Lie group with a given Lie algebra as its Lie algebra or whether there exists such a Lie group at all. We will show in this paper how to construct some Weil prolongations of this mythical Lie group from a given Lie algebra. We will do so within our favorite framework of synthetic dierential geometry.
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