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.

DOI: http://dx.doi.org/10.7900/jot.2011jul08.1912
Keywords: crossed product, compact group, irreducible representation, induced representation, strong-EHI

Contents Full-Text PDF