2006/12/18 by Christoph Wockel · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math-ph #math.DG #math.GR #math.MP #msc:22E65 #msc:55Q52 #msc:81R10
paper · pdf · doi:10.1016/j.jfa.2007.05.016
published as J. Funct. Anal. 251 (2007) 254-288
arxiv created 2006/12/18 · openalex publication_date 2007/07/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on the group of vertical bundle automorphisms Gau(P). Then the full automorphism group Aut(P) is considered as an extension of the open subgroup Diff(M)P of diffeomorphisms of M preserving the equivalence class of P under pull-backs, by the gauge group Gau(P). We derive explicit conditions for the extensions of these Lie group structures, show the smoothness of some natural actions and relate our results to affine Kac--Moody algebras and groups.