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Pictures for Operator Algebras: higher rank graphs

Title
Pictures for Operator Algebras: higher rank graphs
Funding
ARC | Discovery Projects
Contract (GA) number
DP0665131
Start Date
2006/01/01
End Date
2008/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP0665131

 

  • Simplicity of 2-graph algebras associated to Dynamical Systems

    We give a combinatorial description of a family of 2-graphs which subsumes those described by Pask, Raeburn and Weaver. Each 2-graph $\Lambda$ we consider has an associated $C^*$-algebra, denoted $C^*(\Lambda)$, which is simple and purely infinite when $\Lambda$ is aperiodic. We give new, straightforward conditions which ensure that $\Lambda$ is aperiodic. These conditions are highly tractable as we only need to consider the finite set of vertices of $\Lambda$ in order to identify aperiodicit...

    C*-algebras of labelled graphs II - Simplicity results

    We prove simplicity and pure infiniteness results for a certain class of labelled graph $C^*$-algebras. We show, by example, that this class of unital labelled graph $C^*$-algebras is strictly larger than the class of unital graph $C^*$-algebras.
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