Abelian extensions of infinite-dimensional Lie groups
by
Karl-Hermann Neeb
Darmstadt University of Technology

The fact that not every locally convex Lie algebra is integrable, i.e., the Lie algebra of a Lie group makes the extension theory of infinite-dimensional group more difficult than in the finite-dimensional case. In this talk we discuss obstructions for the integrability of abelian extensions of Lie algebras to integrate to corresponding Lie group extensions. These obstructions have a very geometric flavour, which is best seen for the group Diff(M) of diffeomorphisms of a compact manifold and the module of smooth functions on M. In this case the automorphism group of an abelian principal bundle P over M is an interesting abelian extension of an open subgroup of Diff(M).

Date received: June 10, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cals-03.