# Rank-two graphs whose C∗-algebras are direct limits of circle algebras

@article{Pask2005RanktwoGW, title={Rank-two graphs whose C∗-algebras are direct limits of circle algebras}, author={David Pask and Iain Raeburn and Mikael R{\o}rdam and Aidan Sims}, journal={Journal of Functional Analysis}, year={2005}, volume={239}, pages={137-178} }

## 69 Citations

### The Noncommutative Geometry of k-graph C*-Algebras

- Mathematics
- 2005

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### Directed graphs and k-graphs: topology of the path space and how it manifests in the associated C*- algebra

- Mathematics
- 2010

Directed graphs and their higher-rank analogues provide an intuitive frame-work for the analysis of a broad class of C ∗ -algebras which we call graph algebras. Kumjian, Pask, Raeburn and Renault…

### 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…

### A family of 2-graphs arising from two-dimensional subshifts

- MathematicsErgodic Theory and Dynamical Systems
- 2009

Abstract Higher-rank graphs (or k-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz–Krieger C*-algebras of Robertson and Steger. Here we consider a…

### $C^*$-algebras associated to coverings of $k$-graphs

- Mathematics, Computer ScienceDocumenta Mathematica
- 2008

This work shows how to realise a direct limit of k-graph algebras under embeddings induced from coverings as the universal algebra of a (k+1-graph) whose universal algebra encodes this embedding.

### Real rank and topological dimension of higher rank graph algebras

- Mathematics
- 2015

We study dimension theory for the $C^*$-algebras of row-finite $k$-graphs with no sources. We establish that strong aperiodicity - the higher-rank analogue of condition (K) - for a $k$-graph is…

### Endomorphisms and Modular Theory of 2-Graph C*-Algebras

- Mathematics
- 2009

In this paper, we initiate the study of endomorphisms and modular theory of the graph C*-algebras $\O_{\theta}$of a 2-graph $\Fth$ on a single vertex. We prove that there is a semigroup isomorphism…

### COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS

- MathematicsJournal of the Australian Mathematical Society
- 2009

Abstract Consider a projective limit G of finite groups Gn. Fix a compatible family δn of coactions of the Gn on a C*-algebra A. From this data we obtain a coaction δ of G on A. We show that the…

### 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…

### Twisted k-Graph Algebras Associated to Bratteli Diagrams

- Mathematics
- 2014

Given a system of coverings of k-graphs, we show that the second cohomology of the resulting (k + 1)-graph is isomorphic to that of any one of the k-graphs in the system, and compute the semifinite…

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