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Journal of Operator Theory

Volume 70, Issue 1, Summer 2013  pp. 259-272.

Covariant representations of $C^*$-dynamical systems with compact groups

Authors Firuz Kamalov
Author institution: Department of Mathematics, Canadian University of Dubai, Dubai, U.A.E.

Summary:  Let $\cp$ be a $\cstar$-dynamical system, where $G$ is compact. We show that every irreducible covariant representation $(\pi, U)$ of $\cp$ is induced from an irreducible covariant representation $(\pi_0, U_0)$ of a subsystem $(A, G_0, \sigma)$ such that $\pi_0$ is a factor representation. We show that if $(\pi, U)$ is an irreducible covariant representation of $(A, G_P, \sigma)$ with $\mathrm{ker}\, \pi=P$, then $\pi$ is a homogenous representation. Hence, $\cp$ satisfies the strong-EHI property.

Keywords:  crossed product, compact group, irreducible representation, induced representation, strong-EHI

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