Periodicity in Rank 2 Graph Algebras

Davidson, Kenneth R. ; Yang, Dilian

Canadian journal of mathematics, Tome 61 (2009) no. 6, pp. 1239-1261

Résumé

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.

Détail

DOI : 10.4153/CJM-2009-058-0

Mots-clés : 47L55, 47L30, 47L75, 46L05, higher rank graph, aperiodicity condition, simple C*-algebra, expectation