Karl-Hermann Neeb

On extensions of infinite-dimensional Lie groups

Extensions of infinite-dimensional Lie group play a crucial role in several branches of mathematics. Central extensions arise naturally in quantum mechanics in the passage from projective representations to unitary representations. In Lie theory extensions arise in the context of the integrability problem: Which Lie algebra corresponds to a global group? And in differential geometry the automorphisms groups of principal bundles are interesting extensions of groups of diffeomorphisms by gauge groups. In the lecture I shall try to describe a uniform perspective on various aspects of Lie group extensions and their geometry.