Dilating covariant representations of the non-commutative disc algebras

Let ϕ be an isometric automorphism of the non-commutative disc algebra An for n 2. We show that every contractive covariant representation of (An,ϕ) dilates to a unitary covariant representation of (On,ϕ). Hence the C∗-envelope of the semicrossed product An ×ϕ Z+ is On ×ϕ Z. © 2010 Elsevier Inc. All rights reserved