Periodicity in Rank 2 Graph Algebras
By K. Davidson, Dilian Yang. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2007
64 citations recorded by the source corpus.
Abstract Kumjian and Pask introduced an aperiodicity condition for higher rank graphs. We present a detailed analysis of when this occurs in certain rank 2 graphs. When the algebra is aperiodic, we give another proof of the simplicity of ${{\text{C}}^{*}}\left( \mathbb{F}_{\theta }^{+} \right)$ . The periodic ${{\text{C}}^{*}}$ -algebras are characterized, and it is shown that ${{\text{C}}^{*}}\left( \mathbb{F}_{\theta }^{+} \right)\,\simeq \,\text{C}\left( \mathbb{T} \right)\,\otimes \,\mathfrak{U}$ where $\mathfrak{A}$ is a simple ${{\text{C}}^{*}}$ -algebra.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/029221a4e7141161498897ca957e06234c0cb3ad
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
- Aidan Sims
- Iain Raeburn
- David Pask
- Toke Meier Carlsen
- G. Pino
- Astrid an Huef
- John Clark
- Alex Kumjian
In Discrete Mathematics and Combinatorics
In Mathematical Physics
- Aidan Sims
- Iain Raeburn
- David Pask
- Toke Meier Carlsen
- Astrid an Huef
- John Clark
- G. Pino
- Samuel B. G. Webster
Citations in the corpus
- 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].”
- Kumjian-Pask algebras of higher-rank graphs (2011, background): “The higher-rank graph C∗-algebras constructed in [21] have generated a great deal of interest among operator algebraists (for example, [13, 20, 27, 36, 39]), and have broadened the class of C∗-algebras that can be realized as graph algebras [14, 21, 25, 26].”
- Homology for higher-rank graphs and twisted C*-algebras (2011, background): “The C-algebras of higher-rank graphs have been studied by numerous authors over the last decade (see, for example, [6, 7, 10, 11, 40, 41, 43]).”
- The primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources ☆ (2013, background): “In [5], Davidson and Yang comprehensively analyse aperiodicity for single-vertex 2-graphs.”