Abstract
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.
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