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

54 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

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10.1142/S0218196712500580

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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.

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

Abstract

Keywords

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