Higher-rank graph C*-algebras: an inverse semigroup and groupoid approach

Cynthia Farthing; Paul S. Muhly; Trent Yeend

doi:10.1007/s00233-005-0512-2

Higher-rank graph C*-algebras: an inverse semigroup and groupoid approach

Cynthia Farthing, Paul S. Muhly, Trent Yeend

Research output: Contribution to journal › Article › peer-review

67 Citations (Scopus)

Abstract

We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.

Original language	English
Pages (from-to)	159-187
Number of pages	29
Journal	Semigroup Forum
Volume	71
Issue number	2
DOIs	https://doi.org/10.1007/s00233-005-0512-2
Publication status	Published - 2005
Externally published	Yes

Keywords

Cuntz-Krieger algebra
graph algebra
groupoid
higher-rank graph
inverse semigroup

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10.1007/s00233-005-0512-2

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title = "Higher-rank graph C*-algebras: an inverse semigroup and groupoid approach",

abstract = "We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.",

keywords = "Cuntz-Krieger algebra, graph algebra, groupoid, higher-rank graph, inverse semigroup",

author = "Cynthia Farthing and Muhly, \{Paul S.\} and Trent Yeend",

year = "2005",

doi = "10.1007/s00233-005-0512-2",

language = "English",

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pages = "159--187",

journal = "Semigroup Forum",

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publisher = "Springer, Springer Nature",

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T1 - Higher-rank graph C*-algebras

T2 - an inverse semigroup and groupoid approach

AU - Farthing, Cynthia

AU - Muhly, Paul S.

AU - Yeend, Trent

PY - 2005

Y1 - 2005

N2 - We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.

AB - We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.

KW - Cuntz-Krieger algebra

KW - graph algebra

KW - groupoid

KW - higher-rank graph

KW - inverse semigroup

UR - https://www.scopus.com/pages/publications/33646595002

U2 - 10.1007/s00233-005-0512-2

DO - 10.1007/s00233-005-0512-2

M3 - Article

AN - SCOPUS:33646595002

SN - 0037-1912

VL - 71

SP - 159

EP - 187

JO - Semigroup Forum

JF - Semigroup Forum

IS - 2

ER -

Higher-rank graph C*-algebras: an inverse semigroup and groupoid approach

Abstract

Keywords

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