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1. CJM 2009 (vol 61 pp. 1239)
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Periodicity in Rank 2 Graph Algebras 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 $\mathrm{C}^*(\mathbb{F}^+_{\theta})$.
The periodic $\mathrm{C}^*$-algebras are characterized, and it is shown
that $\mathrm{C}^*(\mathbb{F}^+_{\theta}) \simeq
\mathrm{C}(\mathbb{T})\otimes\mathfrak{A}$
where $\mathfrak{A}$ is a simple $\mathrm{C}^*$-algebra.
Keywords:higher rank graph, aperiodicity condition, simple $\mathrm{C}^*$-algebra, expectation Categories:47L55, 47L30, 47L75, 46L05 |