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

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

2009-04-19

arxiv.org/abs/0904.2876v1

Mathematics

Operator Algebras

14 pages

Scientific paper

Assume that $\phi_1$ and $\phi_2$ are automorphisms of the non-commutative disc algebra $\fA_n$, $n \geq 2$. We show that the semicrossed products $\fA_n \times_{\phi_1} \bZ^+$ and $\fA_n \times_{\phi_2} \bZ^+$ are isomorphic as algebras if and only if $\phi_1$ and $\phi_2$ are conjugate via an automorphism of $\fA_n$. A similar result holds for semicrossed products of the d-shift algebra $\A_d$, $d \geq 2$.

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