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 language | English |
|---|---|
| Pages (from-to) | 279–304 |
| Number of pages | 26 |
| Journal | Journal of Noncommutative Geometry |
| Volume | 15 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 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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Mark Lawson
- School of Mathematical & Computer Sciences - Professor
- School of Mathematical & Computer Sciences, Mathematics - Professor
Person: Academic (Research & Teaching)