76 citations · 782 across the 86 of their papers we have counts for
6 papers · 1 filter
When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional?
D. Gwion Evans, Aidan Sims
We investigate the question: when is a higher-rank graph C*-algebra approximately finite dimensional? We prove that the absence of an appropriate higher-rank analogue of a cycle is…
An equivalence theorem for reduced Fell bundle C*-algebras
Aidan Sims, Dana P. Williams
We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full…
On some fundamental results about higher-rank graphs and their C*-algebras
Robert Hazlewood, Iain Raeburn, Aidan Sims +1
Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of…
Homology for higher-rank graphs and twisted C*-algebras
Alex Kumjian, David Pask, Aidan Sims
We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coinc…
A groupoid generalization of Leavitt path algebras
Lisa Orloff Clark, Cynthia Farthing, Aidan Sims +1
Let G be a locally compact, Hausdorff groupoid in which s is a local homeomorphism and the unit space is totally disconnected. Assume there is a continuous cocycle c from G into a…
Co-universal C*-algebras associated to aperiodic k-graphs
Sooran Kang, Aidan Sims
We construct a representation of each finitely aligned aperiodic k-graph Λ on the Hilbert space H^{ap} with basis indexed by aperiodic boundary paths in Λ. We show that the canonic…