Semicrossed products of simple C*-algebras

TL;DR

This paper characterizes when semicrossed products of simple C*-algebras are isometrically isomorphic, showing it occurs precisely when the underlying dynamical systems are outer conjugate.

Contribution

It establishes a complete classification of semicrossed products of simple C*-algebras via outer conjugacy of the dynamical systems.

Findings

Semicrossed products are isometrically isomorphic iff the systems are outer conjugate.

Provides a classification criterion for semicrossed products of simple C*-algebras.

Connects algebraic isomorphism with dynamical system conjugacy.

Abstract

Let $(\A, \alpha)$ and $(\B, \beta)$ be C*-dynamical systems and assume that $\A$ is a separable simple C*-algebra and that $\alpha$ and $\beta$ are *-automorphisms. Then the semicrossed products $\A \times_{\alpha} \bbZ^{+}$ and $\B \times_{\beta} \bbZ^{+}$ are isometrically isomorphic if and only if the dynamical systems $(\A, \alpha)$ and $(\B, \beta)$ are outer conjugate.