The representation of Lie groups by bundle maps

This paper deals with representations of connected Lie groups by bundle maps of fiber bundles. It is pointed out that a large class of such representations can be obtained from the bundle structure theroem, and explicit constructions are given, first on principal bundles and then on associated bundles. Examples are provided to show that, for bundle representations, the theorem of full reducibility breaks down even for compact Lie groups. Finally, a general construction is given for obtaining representations of a Lie group on an arbitrary principal bundle. However, it is not known whether this exhausts all possibilities.