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Periodicity in Rank 2 Graph Algebras

Published online by Cambridge University Press:  20 November 2018

Kenneth R. Davidson  and
Dilian Yang
Kenneth R. Davidson
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1 email: krdavids@uwaterloo.ca
Dilian Yang
Affiliation:
Department of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4 email: dyang@uwindsor.ca
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Abstract

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Kumjian and Pask introduced an aperiodicity condition for higher rank graphs. We present a detailed analysis of when this occurs in certain rank 2 graphs. When the algebra is aperiodic, we give another proof of the simplicity of ${{\text{C}}^{*}}\left( \mathbb{F}_{\theta }^{+} \right)$. The periodic ${{\text{C}}^{*}}$-algebras are characterized, and it is shown that ${{\text{C}}^{*}}\left( \mathbb{F}_{\theta }^{+} \right)\,\simeq \,\text{C}\left( \mathbb{T} \right)\,\otimes \,\mathfrak{U}$ where $\mathfrak{A}$ is a simple ${{\text{C}}^{*}}$-algebra.

Keywords

47L5547L3047L7546L05higher rank graphaperiodicity conditionsimple C*-algebraexpectation
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 6 , 01 December 2009 , pp. 1239 - 1261
Copyright
Copyright © Canadian Mathematical Society 2009

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