Inverse semigroups associated with labelled spaces and their tight spectra

Abstract

The notion of a labelled space was introduced by Bates and Pask in generalizing certain classes of C*-algebras. Motivated by Exel's work on inverse semigroups and combinatorial C*-algebras, we associate each weakly left resolving labelled space with an inverse semigroup, and characterize the tight spectrum of the latter in a way that is reminiscent of the description of the boundary path space of a directed graph.