Pro-Lie groups which are infinite-dimensional Lie groups

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dc.creatorHofmann, K. H.
dc.creatorNeeb, K. -H.
dc.date2006-09-25
dc.date.accessioned2026-07-07T07:25:12Z
dc.date.available2026-07-07T07:25:12Z
dc.descriptionA pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this note we show that a pro-Lie group $G$ is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if $G$ is locally contractible. We also characterize the corresponding pro-Lie algebras in various ways. Furthermore, we characterize those pro-Lie groups which are locally exponential, that is, they are Lie groups with a smooth exponential function which maps a zero neighborhood in the Lie algebra diffeomorphically onto an open identity neighborhood of the group.
dc.identifierhttps://arxiv.org/abs/math/0609684
dc.identifierhttp://arxiv.org/abs/math/0609684
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116641
dc.subjectGroup Theory
dc.subject22E65; 17B65; 22D05
dc.titlePro-Lie groups which are infinite-dimensional Lie groups
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