The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations (Q2043510)

Summary: 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.