A noncommutative generalization of stone duality

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35 Citations (Scopus)


We prove that the category of boolean inverse monoids is dually equivalent to the category of boolean groupoids. This generalizes the classical Stone duality between boolean algebras and boolean spaces. As an instance of this duality, we show that the boolean inverse monoid Cn associated with the Cuntz groupoid Gn is the strong orthogonal completion of the polycyclic (or Cuntz) monoid Pn. The group of units of Cn is the Thompson group Vn,1. Copyright © Australian Mathematical Publishing Association Inc. 2010.

Original languageEnglish
Pages (from-to)385-404
Number of pages20
JournalJournal of the Australian Mathematical Society
Issue number3
Publication statusPublished - Jun 2010


  • étale topological groupoid
  • inverse semigroup
  • stone duality


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