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.
|Number of pages||16|
|Journal||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|State||Published - Feb 2021|
Bibliographical noteFunding Information:
The first author was supported by an NSF grant DMS-1900916 and by the European Union’s Horizon 2020 Marie Sklodowska-Curie grant No 839412.
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.
- Cuntz Krieger
- Cyclic decomposition
- Directed graphs
- Free semigroupoid algebra
- Graph algebra
- Road colouring
ASJC Scopus subject areas
- Mathematics (all)