  In this paper the space of almost commuting elements in a Lie group is
studied through a homotopical point of view. In particular a stable splitting
after one suspension is derived for these spaces and their quotients under
conjugation. A complete description for the stable factors appearing in this
splitting is provided for compact connected Lie groups of rank one.By using
symmetric products, the colimits $\Rep(\Z^n, SU)$, $\Rep(\Z^n,U)$ and
$\Rep(\Z^n, Sp)$ are explicitly described as finite products of
Eilenberg-MacLane spaces.
