The universal Boolean inverse semigroup presented by the abstract Cuntz–Krieger relations

Mark V. Lawson, Alina Vdovina

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Abstract

This paper is a contribution to the theory of what might be termed 0-dimensional non-commutative spaces. We prove that associated with each inverse semigroup S is a Boolean inverse semigroup presented by the abstract versions of the Cuntz–Krieger relations. We call this Boolean inverse semigroup the tight completion of S and show that it arises from Exel's tight groupoid under non-commutative Stone duality.
Original languageEnglish
Pages (from-to)279–304
Number of pages26
JournalJournal of Noncommutative Geometry
Volume15
Issue number1
DOIs
Publication statusPublished - 21 Apr 2021

Keywords

  • Ample groupoids
  • Cuntz–Krieger relations
  • Inverse semigroups
  • Stone duality

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Mathematical Physics
  • Geometry and Topology

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