Periodicity in Rank 2 Graph Algebras

Abstract

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 C*(𝔽+θ). The periodic C*-algebras are characterized, and it is shown that C*(𝔽+θ) ≃ C(𝕋) ⊗ 𝒰 where 𝒰 is a simple C*-algebra.