Dilating covariant representations of the non-commutative disc algebras

Abstract

Let $\varphi$ be an isometric automorphism of the non-commutative disc algebra $\fA_n$ for $n\ge 2$. We show that every contractive covariant representation of $(\fA_n, ϕ)$ dilates to a unitary covariant representation of $({Ø}_n,\varphi )$. Hence the C*-envelope of the semicrossed product $\fA_n \times_ϕ \bZ^+$ is $Ø_n \times_ϕ \bZ$.

18 pages