From Lie algebras to Lie groups within synthetic differential geometry: Weil sprouts of Lie's third fundamental theorem

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2013
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Mark
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Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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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.
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Mathematics for Applications. 2013, 2, č. 2, s. 135-151. ISSN 1805-3629.
http://ma.fme.vutbr.cz/archiv/2_2/ma_2_2_nishimura_final.pdf
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en
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© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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