Lie group structures on symmetry groups of principal bundles

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 over the compact manifold M. This is done by first considering Lie group structures on the group of vertical bundle automorphisms . Then the full automorphism group is considered as an extension of the open subgroup of diffeomorphisms of M preserving the equivalence class of under pull-backs, by the gauge group . 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. [Copyright &y& Elsevier]