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

By David Pask, Iain Raeburn, M. Rørdam, Aidan Sims. 2005

74 citations recorded by the source corpus.

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Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a788c160bf7606ffb2e4a33bff7428f60b45e582

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Aidan Sims
2. Iain Raeburn
3. David Pask
4. A. Rennie
5. R. Exel
6. G. Pino
7. Samuel B. G. Webster
8. Astrid an Huef

In Geometry and Topology

1. Aidan Sims
2. Iain Raeburn
3. David Pask
4. Samuel B. G. Webster
5. R. Hazlewood
6. A. Rennie
7. G. Pino
8. Astrid an Huef

In Mathematical Physics

1. Aidan Sims
2. Iain Raeburn
3. David Pask
4. A. Rennie
5. Jack Spielberg
6. R. Exel
7. Astrid an Huef
8. John Clark

Citations in the corpus

• Kumjian-Pask algebras of higher-rank graphs (2011, methodology): “1], but since [25] uses a different formulation of aperiodicity, we also have to invoke the equivalence of the different notions of aperiodicity [32, Lemma 3.”
• Inverse semigroups and combinatorial C*-algebras (2007, background): “C*-algebras [2, 3, 14, 15, 18, 25, 29, 30, 35], including the case of higher rank graphs introduced by Kumjian and Pask in [16], and given its final form by Farthing, Muhly and Yeend in [13]. See also [17, 22, 23, 28]. The monograph [27] is an excellent source of well organized information and refere”
• Groupoids and C * -algebras for categories of paths (2011, background): “ very important classes: AF algebras, and Kirchberg algebras having free K1 group, are the most notable. Yet it remains a fairly limited class. Already the 2-graphs exhibit much richer behavior (e.g. [20]). Higher-rank graphs, on the other hand, are quite rigid objects, and difficult to construct. (It”
• Remarks on some fundamental results about higher-rank graphs and their C*-algebras (2011, background): “C∗-algebras associated to graphs and k-graphs have attracted significant attention recently because they at once encompass a great many interesting examples [2, 6, 11, 17], and are remarkably tractable [3, 4, 5, 7, 12, 13, 21].”
• The Noncommutative Geometry of k-graph C*-Algebras (2005, methodology): “example, [ PRRS ] contains many examples of 2-graphs which admit faithful graph traces and whose C ∗ -algebras are simple AT algebras with real rank 0. However, our condition is a direct”