The second Takagi Lectures
May 26, 2007 (Sat) 17:00--18:00
May 27, 2007 (Sun) 13:30--14:30
Graduate School of Mathematical Sciences,
The University of Tokyo

Towards a Lie theory of locally convex groups
K.-H. Neeb
(Technische Universität Darmstadt)

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie subgroups, and integrability of Lie algebra extensions to Lie group extensions. We further describe how regularity or local exponentiality of a Lie group can be used to obtain quite satisfactory answers to some of the fundamental problems. These results are illustrated by specialization to some specific classes of Lie groups, such as direct limit groups, linear Lie groups, groups of smooth maps and groups of diffeomorphisms.

References: K.-H. Neeb, Towards a Lie theory of locally convex groups,
Japanese Journal of Mathematics, Volume 1-2, (2006), pages 291--468.
[Article (Springer Link)]