  We provide new arguments to see topological Kac-Moody groups as generalized
semisimple groups over local fields: they are products of topologically simple
groups and their Iwahori subgroups are the normalizers of the pro-p Sylow
subgroups. We use a dynamical characterization of parabolic subgroups to prove
that some countable Kac-Moody groups with Fuchsian buildings are not linear. We
show for this that the linearity of a countable Kac-Moody group implies the
existence of a closed embedding of the corresponding topological group in a
non-Archimedean simple Lie group, thanks to a commensurator super-rigidity
theorem proved in the Appendix by P. Bonvin.
