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

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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 languageEnglish
Article number1250058
Number of pages47
JournalInternational Journal of Algebra and Computation
Volume22
Issue number6
DOIs
Publication statusPublished - Sep 2012

Keywords

  • Etale topological groupoid
  • C*-algebra
  • inverse semigroup

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