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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