Ergodic Actions of Convergent Fuchsian groups on quotients of the noncommutative Hardy algebras

We establish that particular quotients of the non-commutative Hardy algebras carry ergodic actions of convergent discrete subgroups of the group $\mathrm{SU}(n,1)$ 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 ${\mathbb{C}}^n$.