arXiv subjects
Publications and source records attributed to E. G. Katsoulis.
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.
Assume that $ϕ_1$ and $ϕ_2$ are automorphisms of the non-commutative disc algebra $\fA_n$, $n \geq 2$. 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 $ϕ_1$ and $ϕ_2$ are conjugate via an automorphism of $\fA_n$. A similar result holds for semicrossed products of the d-shift algebra $\A_d$, $d \geq 2$.
Let $ϕ$ be an isometric automorphism of the non-commutative disc algebra $\fA_n$ for $n \geq 2$. We show that every contractive covariant representation of $(\fA_n, ϕ)$ dilates to a unitary covariant representation of $(Ø_n, ϕ)$. Hence the C*-envelope of the semicrossed product $\fA_n \times_ϕ \bZ^+$ is $Ø_n \times_ϕ \bZ$.