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.

OriginalsprogEngelsk
TidsskriftProceedings of the Royal Society of Edinburgh Section A: Mathematics
Vol/bind151
Udgave nummer1
Sider (fra-til)391-406
ISSN0308-2105
DOI
StatusUdgivet - 2021

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