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Full-Text Articles in Science and Technology Studies
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Faculty of Engineering and Information Sciences - Papers: Part A
We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterises the higher-rank graphs that admit a nontrivial Cuntz-Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the C*-algebras generated by Cuntz-Krieger families.
Actions Of Z^K Associated To Higher Rank Graphs, Alexander Kumjian, David Pask
Actions Of Z^K Associated To Higher Rank Graphs, Alexander Kumjian, David Pask
Faculty of Engineering and Information Sciences - Papers: Part A
An action of Zk is associated to a higher rank graph Λ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We show that the stable Ruelle algebra of Λ is strongly Morita equivalent to C∗(Λ). Hence, if Λ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.