Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras

Mark Lawson

doi:10.1142/S0218196712500580

Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras

Mark Lawson

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

57 Citations (Scopus)

Abstract

We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups with a class of etale topological groupoids. We show how the Thompson-Higman groups arise via this construction as well as a range of important C*-algebras such as the Cuntz and Cuntz-Krieger C*-algebras.

Original language	English
Article number	1250058
Number of pages	47
Journal	International Journal of Algebra and Computation
Volume	22
Issue number	6
DOIs	https://doi.org/10.1142/S0218196712500580
Publication status	Published - Sept 2012

Keywords

Etale topological groupoid
C*-algebra
inverse semigroup

Access to Document

10.1142/S0218196712500580

Cite this

@article{ac893cc776ed494591bb9e9f340fcc89,

title = "Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras",

abstract = "We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups with a class of etale topological groupoids. We show how the Thompson-Higman groups arise via this construction as well as a range of important C*-algebras such as the Cuntz and Cuntz-Krieger C*-algebras. ",

keywords = "Etale topological groupoid, C*-algebra, inverse semigroup",

author = "Mark Lawson",

year = "2012",

month = sep,

doi = "10.1142/S0218196712500580",

language = "English",

volume = "22",

journal = "International Journal of Algebra and Computation",

issn = "0218-1967",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "6",

}

TY - JOUR

T1 - Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras

AU - Lawson, Mark

PY - 2012/9

Y1 - 2012/9

N2 - We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups with a class of etale topological groupoids. We show how the Thompson-Higman groups arise via this construction as well as a range of important C*-algebras such as the Cuntz and Cuntz-Krieger C*-algebras.

AB - We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups with a class of etale topological groupoids. We show how the Thompson-Higman groups arise via this construction as well as a range of important C*-algebras such as the Cuntz and Cuntz-Krieger C*-algebras.

KW - Etale topological groupoid

KW - C-algebra

KW - inverse semigroup

U2 - 10.1142/S0218196712500580

DO - 10.1142/S0218196712500580

M3 - Article

SN - 0218-1967

VL - 22

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 6

M1 - 1250058

ER -

Non-commutative Stone duality: inverse semigroups, topological groupoids and C*-algebras

Abstract

Keywords

Access to Document

Fingerprint

Cite this