Biholomorphisms of the unit ball of C^n and semicrossed products

Abstract

Assume that ${\varphi }_1$ and ${\varphi }_2$ are automorphisms of the non-commutative disc algebra $\fA_n$, $n\ge 2$. We show that the semicrossed products $\fA_n \times_{ϕ_1} \bZ^+$ and $\fA_n \times_{ϕ_2} \bZ^+$ are isomorphic as algebras if and only if ${\varphi }_1$ and ${\varphi }_2$ are conjugate via an automorphism of $\fA_n$. A similar result holds for semicrossed products of the d-shift algebra $\A_d$, $d\ge 2$.

14 pages

References in corpus (1)

• Operator algebras associated with unitary commutation relations