All finite transitive graphs admit a self-adjoint free semigroupoid algebra
Research output: Contribution to journal › Journal article › Research › peer-review
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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Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
Volume | 151 |
Issue number | 1 |
Pages (from-to) | 391-406 |
ISSN | 0308-2105 |
DOIs | |
Publication status | Published - 2021 |
- Cuntz Krieger, Cyclic decomposition, Directed graphs, Free semigroupoid algebra, Graph algebra, Periodic, Road colouring
Research areas
Links
- https://arxiv.org/pdf/1811.11058.pdf
Accepted author manuscript
ID: 243064417