Fundamental groupoids of k-graphs

David Pask; John Quigg; Iain Raeburn

Fundamental groupoids of k-graphs

David Pask, John Quigg, Iain Raeburn

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Review article › peer-review

13 Scopus citations

Abstract

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their fundamental groupoids.

Original language	English (US)
Pages (from-to)	195-207
Number of pages	13
Journal	New York Journal of Mathematics
Volume	10
State	Published - Jul 30 2004

Keywords

Directed graph
Fundamental group
Groupoid
Small category
k-graph

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "Fundamental groupoids of k-graphs",

abstract = "k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their fundamental groupoids.",

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AU - Pask, David

AU - Quigg, John

AU - Raeburn, Iain

PY - 2004/7/30

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N2 - k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their fundamental groupoids.

AB - k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their fundamental groupoids.

KW - Directed graph

KW - Fundamental group

KW - Groupoid

KW - Small category

KW - k-graph

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M3 - Review article

AN - SCOPUS:4644303814

SN - 1076-9803

VL - 10

SP - 195

EP - 207

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

ER -

Fundamental groupoids of k-graphs

Abstract

Keywords

ASJC Scopus subject areas

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