Simplicity of ultragraph algebras

By M. Tomforde. 2001

47 citations recorded by the source corpus.

In this paper we analyze the structure of C*-algebras associated to ultragraphs, which are generalizations of directed graphs. We characterize the simple ultragraph algebras as well as deduce necessary and sufficient conditions for an ultragraph algebra to be purely infinite and to be AF. Using these techniques we also produce an example of an ultragraph algebra that is neither a graph algebra nor an Exel-Laca algebra. We conclude by proving that the C*-algebras of ultragraphs with no sinks are Cuntz-Pimsner algebras.

Subfields: Algebra and Number Theory, Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/841eb58d065bc2db5788a62e5831d8a59f45fccc

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. D. Royer
2. D. Gonccalves
3. M. Tomforde
4. G. Abrams
5. G. Pino
6. Aidan Sims
7. Vern I. Paulsen
8. L. O. Clark

In Atomic and Molecular Physics, and Optics

1. D. Royer
2. D. Gonccalves
3. M. Tomforde

In Mathematical Physics

1. D. Royer
2. D. Gonccalves
3. M. Tomforde
4. G. Abrams
5. G. Pino
6. Aidan Sims
7. Vern I. Paulsen
8. L. O. Clark

Citations in the corpus

• Infinite alphabet edge shift spaces via ultragraphs and their C*-algebras (2017, background): “The associated C*-algebras form a class that strictly contain graph C*-algebras and the Exel-Laca algebras, see [29, 30].”
• A unified approach to Exel-Laca algebras and C*-algebras associated to graphs (2001, background): “Furthermore, it is shown in a forthcoming article ([18]) that there exist ultragraph algebras that are neither Exel-Laca algebras nor graph algebras.”