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

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Standard

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 tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Dor-On, A & Linden, C 2021, 'All finite transitive graphs admit a self-adjoint free semigroupoid algebra', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, bind 151, nr. 1, s. 391-406. https://doi.org/10.1017/prm.2020.20

APA

Dor-On, A., & Linden, C. (2021). All finite transitive graphs admit a self-adjoint free semigroupoid algebra. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 151(1), 391-406. https://doi.org/10.1017/prm.2020.20

Vancouver

Dor-On A, Linden C. All finite transitive graphs admit a self-adjoint free semigroupoid algebra. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2021;151(1):391-406. https://doi.org/10.1017/prm.2020.20

Author

Dor-On, Adam ; Linden, Christopher. / All finite transitive graphs admit a self-adjoint free semigroupoid algebra. I: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2021 ; Bind 151, Nr. 1. s. 391-406.

Bibtex

@article{2d8062ff51494dc9b918ea684435fa60,
title = "All finite transitive graphs admit a self-adjoint free semigroupoid algebra",
abstract = "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 B{\'e}al 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.",
keywords = "Cuntz Krieger, Cyclic decomposition, Directed graphs, Free semigroupoid algebra, Graph algebra, Periodic, Road colouring",
author = "Adam Dor-On and Christopher Linden",
year = "2021",
doi = "10.1017/prm.2020.20",
language = "English",
volume = "151",
pages = "391--406",
journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",
issn = "0308-2105",
publisher = "The/R S E Scotland Foundation",
number = "1",

}

RIS

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