  We show that the dynamical symmetry of the hydrogen atom leads in a natural
way to an infinite-dimensional algebra, which we identify as the positive
subalgebras of twisted Kac-Moody algebras of $ so(4)$. We also generalize our
results to the $N$-dimensional hydrogen atom. For odd $N$, we identify the
dynamical algebra with the positive part of the twisted algebras $\hat
{so}(N+1)^\tau$. However, for even $N$ this algebra corresponds to a parabolic
subalgebra of the untwisted loop algebra $\hat{so}(N+1)$.
