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

TL;DR

This paper demonstrates that certain quotients of non-commutative Hardy algebras exhibit ergodic actions under convergent Fuchsian groups, linking operator algebra spectra with complex geometric automorphisms.

Contribution

It introduces a method to compute spectra of these quotients and characterizes their automorphisms via biholomorphic maps of the unit ball.

Findings

Quotients of non-commutative Hardy algebras carry ergodic actions.

Spectra of quotients can be explicitly computed.

Automorphisms correspond to biholomorphic maps of the unit ball.

Abstract

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 $\mathbb{C}^{n}$.