# 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} }

## 13 Citations

### Isomorphism of the cubical and categorical cohomology groups of a higher-rank graph

- MathematicsTransactions of the American Mathematical Society, Series B
- 2021

We use category-theoretic techniques to provide two proofs showing that for a higher-rank graph
Λ
\Lambda
, its cubical (co-)homology and categorical (co-)homology groups are isomorphic in…

### Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras

- MathematicsIndiana University Mathematics Journal
- 2022

We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a…

### Structure theory and stable rank for C*-algebras of finite higher-rank graphs

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2021

Abstract We study the structure and compute the stable rank of $C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the $C^{*}$-algebra when the $k$-graph either…

### AF‐embeddable labeled graph C∗ ‐algebras

- MathematicsBulletin of the London Mathematical Society
- 2020

AF‐embeddability, quasidiagonality and stable finiteness of a C∗ ‐algebra have been studied by many authors and shown to be equivalent for certain classes of C∗ ‐algebras. The crossed products…

### Unbounded quasitraces, stable finiteness and pure infiniteness

- Mathematics
- 2017

We prove that if A is a \sigma-unital exact C*-algebra of real rank zero, then every state on K_0(A) is induced by a 2-quasitrace on A. This yields a generalisation of Rainone's work on pure…

### Spectral triples for higher-rank graph $C^*$-algebras

- Mathematics
- 2018

In this note, we present a new way to associate a spectral triple to the noncommutative $C^*$-algebra $C^*(\Lambda)$ of a strongly connected finite higher-rank graph $\Lambda$. We generalize a…

### Subalgebras of simple AF-algebras

- Mathematics
- 2018

It is shown that if A is a separable, exact C*-algebra which satisfies the Universal Coefficient Theorem (UCT) and has a faithful, amenable trace, then A admits a trace-preserving embedding into a…

### Dense subalgebras of purely infinite simple groupoid C*-algebras

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2020

Abstract A simple Steinberg algebra associated to an ample Hausdorff groupoid G is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space…

### Wavelets and spectral triples for higher-rank graphs

- Mathematics
- 2017

In this paper, we present two new ways to associate a spectral triple to a higher-rank graph $\Lambda$. Moreover, we prove that these spectral triples are intimately connected to the wavelet…

### Spectral triples and wavelets for higher-rank graphs

- MathematicsJournal of Mathematical Analysis and Applications
- 2020

## References

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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…

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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…