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Periodicity in Rank 2 Graph Algebras

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Type
Preprint
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Submission Date
Identifiers
arXiv ID: 0705.4499
Source
arXiv
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Unknown
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Abstract

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 $\ca(\Fth)$. The periodic C*-algebras are characterized, and it is shown that $\ca(\Fth) \simeq \rC(\bT) \otimes \fA$ where $\fA$ is a simple C*-algebra.

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