Kumjian-Pask algebras of higher-rank graphs

By G. Pino, John Clark, Astrid an Huef, Iain Raeburn. 2011

89 citations recorded by the source corpus.

We introduce higher-rank analogues of the Leavitt path algebras, which we call the Kumjian-Pask algebras. We prove graded and Cuntz-Krieger uniqueness theorems for these algebras, and analyze their ideal structure.

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

View Paper: https://www.semanticscholar.org/paper/3cd6319961e80c15f6e4c04336fb8a4708b7289e

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. Cynthia Farthing
4. J. Brown
5. G. Abrams
6. Ben Steinberg
7. Roozbeh Hazrat
8. M. Tomforde

In Geometry and Topology

1. Aidan Sims
2. G. Abrams
3. L. O. Clark
4. Ben Steinberg
5. Trent Yeend

In Mathematical Physics

1. Aidan Sims
2. L. O. Clark
3. Cynthia Farthing
4. J. Brown
5. G. Abrams
6. Ben Steinberg
7. Roozbeh Hazrat
8. M. Tomforde

Citations in the corpus

• Simplicity of algebras associated to étale groupoids (2012, background): “escribe inverse-semigroup algebras. These algebras, which we call Steinberg algebras, were also examined in [7] where they are shown to include the complex Kumjian-Pask algebras of higher-rank graphs [4], and hence the complex Leavitt path algebras of directed graphs [1]. In general, A(G) is dense i”
• Leavitt path algebras: the first decade (2014, background): “• C-algebras of higher rank graphs were formalized in [73] (2000); the corresponding KumjianPask algebras were introduced in [40] (2014).”