# 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.