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 |
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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 - 1 Feb 2021 |
Externally published | Yes |
Keywords
- Cuntz Krieger
- Cyclic decomposition
- Directed graphs
- Free semigroupoid algebra
- Graph algebra
- Periodic
- Road colouring
ASJC Scopus subject areas
- General Mathematics