From Lie algebras to Lie groups within synthetic differential geometry: Weil sprouts of Lie's third fundamental theorem
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Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of in nite-dimensional 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 di erential geometry.
Document typePeer reviewed
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SourceMathematics for Applications. 2013, 2, č. 2, s. 135-151. ISSN 1805-3629.
- 2013/2