FROM LIE ALGEBRAS TO LIE GROUPS WITHIN SYNTHETIC DIFFERENTIAL GEOMETRY: WEIL SPROUTS OF LIE'S THIRD FUNDAMENTAL THEOREM

DOI10.13164/MA.2013.11zbMATH Open1300.22005arXiv1307.5520OpenAlexW2963196546WikidataQ115238891 ScholiaQ115238891MaRDI QIDQ5168361

Hirokazu Nishimura

Publication date: 3 July 2014

Published in: Mathematics for Application (Search for Journal in Brave)

Abstract: Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of infinite-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 differential geometry.

Full work available at URL: https://arxiv.org/abs/1307.5520

zbMATH Keywords

Lie groupBaker-Campbell-Hausdorff formulasynthetic differential geometryLie's third fundamental theoremWeil prolongation

Mathematics Subject Classification ID

General properties and structure of real Lie groups (22E15) Topos-theoretic approach to differentiable manifolds (58A03)

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