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# Classification of Inductive Limits of Outer Actions of ${\mathbb R}$ on Approximate Circle Algebras

Published:2011-03-24
Printed: Mar 2012
• Andrew J. Dean,
Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON, P7B 5E1
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## Abstract

In this paper we present a classification, up to equivariant isomorphism, of $C^*$-dynamical systems $(A,{\mathbb R},\alpha )$ arising as inductive limits of directed systems $\{ (A_n,{\mathbb R},\alpha_n),\varphi_{nm}\}$, where each $A_n$ is a finite direct sum of matrix algebras over the continuous functions on the unit circle, and the $\alpha_n$s are outer actions generated by rotation of the spectrum.
 Keywords: classification, $C^*$-dynamical system
 MSC Classifications: 46L57 - Derivations, dissipations and positive semigroups in $C^*$-algebras 46L35 - Classifications of $C^*$-algebras

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