Groupoid models for the C*-algebras of topological higher-rank graphs

By Trent Yeend. 2006

79 citations recorded by the source corpus.

We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamical systems to our setting, we prove results on essential freeness and amenability of the groupoids which capture the existing theory, and extend results involving group crossed products of graph algebras.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/81a42f4322081c2c704b264ba383a40280db4f0c

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. L. O. Clark
3. Toke Meier Carlsen
4. Nathan Brownlowe
5. J. Brown
6. Michael F. Whittaker
7. Cynthia Farthing
8. Ben Steinberg

In Mathematical Physics

1. Aidan Sims
2. Toke Meier Carlsen
3. L. O. Clark
4. Nathan Brownlowe
5. J. Brown
6. Michael F. Whittaker
7. Cynthia Farthing
8. Ben Steinberg

In Statistical and Nonlinear Physics

1. Nathan Brownlowe
2. Aidan Sims
3. J. Brown
4. Michael F. Whittaker
5. L. O. Clark
6. Toke Meier Carlsen
7. Cynthia Farthing

Citations in the corpus

• Equivalent groupoids have Morita equivalent Steinberg algebras (2013, unknown): “a groupoid GE from a graph Ecan be found in [15]. This generalises the construction in [13]. Unlike [13] and [15], we do not require our graphs to be countable. More general versions are described in [9, 12, 18, 26]. Define X:= E∞ ∪ {µ∈ E ∗| s E(µ) is a source}∪ {µ∈ E | sE(µ) is an infinite receiver}.”
• Graph algebras and orbit equivalence (2014, background): “Their construction has been generalized to compactly aligned topological k-graphs in [26].”
• Simplicity of algebras associated to étale groupoids (2012, background): “There are many classes of C-algebras with étale groupoid models (see for example [8, 11, 13, 14, 16, 19, 26, 28, 31, 36]), so we expect that our results will find numerous applications.”