AF-embeddability of 2-graph algebras and quasidiagonality of k-graph algebras
@article{Clark2015AFembeddabilityO2, title={AF-embeddability of 2-graph algebras and quasidiagonality of k-graph algebras}, author={Lisa Orloff Clark and Astrid an Huef and Aidan Sims}, journal={Journal of Functional Analysis}, year={2015}, volume={271}, pages={958-991} }
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References
SHOWING 1-10 OF 34 REFERENCES
Cuntz-Krieger Algebras of Infinite Graphs and Matrices
- Mathematics
- 2003
We show that the Cuntz-Krieger algebras of infinite graphs and infinite {0,1}-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness…
Simplicity of C*‐algebras associated to higher‐rank graphs
- Mathematics
- 2007
We prove that if Λ is a row‐finite k‐graph with no sources, then the associated C*‐algebra is simple if and only if Λ is cofinal and satisfies Kumjian and Pask's aperiodicity condition, known as…
Higher Rank Graph C-Algebras
- Mathematics
- 2000
Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that of…
On Quasidiagonal C*-algebras
- Mathematics
- 2000
We give a detailed survey of the theory of quasidiagonal C*-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular…
AF Embeddability of Crossed Products of AF Algebras by the Integers
- Mathematics
- 1997
IfAis an AF algebra andα∈Aut(A), it is shown that AF embeddability of the crossed product,A×αZ, is equivalent toA×αZ being stably finite. This equivalence follows from a simple K-theoretic…
AF-Embeddings of Graph Algebras
- Mathematics
- 2014
Let $E$ be a countable directed graph. We show that $C^*(E)$ is AF-embeddable if and only if no loop in $E$ has an entrance. The proof is constructive and is in the same spirit as the Drinen-Tomforde…
The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆
- Mathematics
- 2014
Remarks on some fundamental results about higher-rank graphs and their C*-algebras
- MathematicsProceedings of the Edinburgh Mathematical Society
- 2013
Abstract 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 the…