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A GENERALISATION OF HIGHER-RANK GRAPHS

Part of: Special categories Selfadjoint operator algebras

Published online by Cambridge University Press:  26 July 2021

MARK V. LAWSON Open the ORCID record for MARK V. LAWSON [Opens in a new window]  and
ALINA VDOVINA Open the ORCID record for ALINA VDOVINA [Opens in a new window]
MARK V. LAWSON*
Affiliation:
Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK
ALINA VDOVINA
Affiliation:
School of Mathematics and Statistics, Herschel Building, Newcastle University, Newcastle-upon-Tyne NE1 7RU, UK e-mail: alina.vdovina@ncl.ac.uk
*
e-mail: m.v.lawson@hw.ac.uk
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Abstract

We introduce ‘generalised higher-rank k-graphs’ as a class of categories equipped with a notion of size. They extend not only higher-rank k-graphs, but also the Levi categories introduced by the first author as a categorical setting for graphs of groups. We prove that examples of generalised higher-rank k-graphs can be constructed using Zappa–Szép products of groupoids and higher-rank graphs.

Keywords

higher-rank graphsZappa–Szép productsC*-algebras

MSC classification

Primary: 18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories)
Secondary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 2 , April 2022 , pp. 257 - 266
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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