1. CJM 2006 (vol 58 pp. 625)
 Mohrdieck, Stephan

A Steinberg Cross Section for NonConnected Affine KacMoody Groups
In this paper we generalise the concept of a Steinberg
cross section to nonconnected affine KacMoody groups.
This Steinberg cross section is a section to the
restriction of the adjoint quotient map to a given exterior
connected component of the affine KacMoody group.
(The adjoint quotient is only defined on a certain submonoid of the
entire group, however, the intersection of this submonoid with each
connected component is nonvoid.)
The image of the Steinberg cross section consists of a
``twisted Coxeter cell'',
a transversal slice to a twisted Coxeter element.
A crucial point in the proof of the main result is that the image of
the cross section can be endowed with a $\Cst$action.
Category:22E67 

2. CJM 2003 (vol 55 pp. 969)
 Glöckner, Helge

Lie Groups of Measurable Mappings
We describe new construction principles for infinitedimensional Lie
groups. In particular, given any measure space $(X,\Sigma,\mu)$ and
(possibly infinitedimensional) Lie group $G$, we construct a Lie
group $L^\infty (X,G)$, which is a Fr\'echetLie group if $G$ is so.
We also show that the weak direct product $\prod^*_{i\in I} G_i$ of an
arbitrary family $(G_i)_{i\in I}$ of Lie groups can be made a Lie
group, modelled on the locally convex direct sum $\bigoplus_{i\in I}
L(G_i)$.
Categories:22E65, 46E40, 46E30, 22E67, 46T20, 46T25 
