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

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

2010-10-28

arxiv.org/abs/1010.5840v1

Proceedings of the AMS 139 (2011) 7, pp. 2485--2496

Mathematics

Operator Algebras

Accepted for publication in Proc. AMS

Scientific paper

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

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