2006/09/25 by Karl H. Hofmann, K. H. Hofmann, Hofmann, K. H. +3
Mathematics · #17B65 #22D05 #22E65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:17B65 #msc:22D05 #msc:22E65
paper · pdf · doi:10.48550/arxiv.math/0609684
arxiv created 2006/09/25 · openalex publication_date 2006/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 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.