Periodicity in Rank 2 Graph Algebras

Details Periodicity in Rank 2 Graph Algebras Periodicity in Rank 2 Graph Algebras

2007-05-31

arxiv.org/abs/0705.4499v1

Mathematics

Operator Algebras

27 pages

Scientific paper

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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