Ergodic actions of convergent Fuchsian groups on quotients of the noncommutative Hardy algebras

Arias, Alvaro; Latrémolière, Frédéric

doi:10.1090/S0002-9939-2011-10794-9

Ergodic actions of convergent Fuchsian groups on quotients of the noncommutative Hardy algebras
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by Alvaro Arias and Frédéric Latrémolière PDF

Proc. Amer. Math. Soc. 139 (2011), 2485-2496 Request permission

Abstract:

We establish that particular quotients of the noncommutative 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 terms of biholomorphic maps of the unit ball in $\mathbb {C}^{n}.$

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