All finite transitive graphs admit a self-adjoint free semigroupoid algebra
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All finite transitive graphs admit a self-adjoint free semigroupoid algebra. / Dor-On, Adam; Linden, Christopher.
I: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Bind 151, Nr. 1, 2021, s. 391-406.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt
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TY - JOUR
T1 - All finite transitive graphs admit a self-adjoint free semigroupoid algebra
AU - Dor-On, Adam
AU - Linden, Christopher
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Cuntz Krieger
KW - Cyclic decomposition
KW - Directed graphs
KW - Free semigroupoid algebra
KW - Graph algebra
KW - Periodic
KW - Road colouring
UR - http://www.scopus.com/inward/record.url?scp=85082646308&partnerID=8YFLogxK
U2 - 10.1017/prm.2020.20
DO - 10.1017/prm.2020.20
M3 - Journal article
AN - SCOPUS:85082646308
VL - 151
SP - 391
EP - 406
JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
SN - 0308-2105
IS - 1
ER -
ID: 243064417