Abstract
In this paper we show that every non-cycle finite transitive directed graph has a Cuntz-Krieger family whose WOT-closed algebra is. This is accomplished through a new construction that reduces this problem to in-degree 2-regular graphs, which is then treated by applying the periodic Road Colouring Theorem of Béal and Perrin. As a consequence we show that finite disjoint unions of finite transitive directed graphs are exactly those finite graphs which admit self-adjoint free semigroupoid algebras.
| Original language | English |
|---|---|
| Pages (from-to) | 391-406 |
| Number of pages | 16 |
| Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
| Volume | 151 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
Keywords
- Cuntz Krieger
- Cyclic decomposition
- Directed graphs
- Free semigroupoid algebra
- Graph algebra
- Periodic
- Road colouring
ASJC Scopus subject areas
- General Mathematics
Fingerprint
Dive into the research topics of 'All finite transitive graphs admit a self-adjoint free semigroupoid algebra'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver