JournalsjncgVol. 15, No. 1pp. 279–304

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

  • Mark V. Lawson

    Heriot-Watt University, Edinburgh, UK
  • Alina Vdovina

    Newcastle University, Newcastle-upon-Tyne, UK
The universal Boolean inverse semigroup presented by the abstract Cuntz–Krieger relations cover
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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 SS 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 SS and show that it arises from Exel's tight groupoid under non-commutative Stone duality.

Cite this article

Mark V. Lawson, Alina Vdovina, The universal Boolean inverse semigroup presented by the abstract Cuntz–Krieger relations. J. Noncommut. Geom. 15 (2021), no. 1, pp. 279–304

DOI 10.4171/JNCG/400