  We establish that particular quotients of the non-commutative Hardy algebras
carry ergodic actions of convergent discrete subgroups of the group
$\operatorname*{SU}(n,1)$ of automorphisms of the unit ball in $\mathbb{C}%
^{n}$. To do so, we provide a mean to compute the spectra of quotients of
noncommutative Hardy algebra and characterize their automorphisms in term of
biholomorphic maps of the unit ball in $\mathbb{C}^{n}$.
