All finite transitive graphs admit a self-adjoint free semigroupoid algebra

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

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.

TidsskriftProceedings of the Royal Society of Edinburgh Section A: Mathematics
Udgave nummer1
Sider (fra-til)391-406
StatusUdgivet - 2021


ID: 243064417