Inverse semigroups associated with labelled spaces and their tight spectra

• DOI: 10.1007/s00233-016-9785-x
• Publication Date: 2016-03-04T17:20:50Z
• Authors: Giuliano Boava; Gilles G. de Castro; Fernando de L. Mo...
• Keywords: 20M18 (Primary), 05C20, 05C78 (Secondary); Rings and Algebras (math.RA); Mathematics - Operator Algebras; FOS: Mathematics; Mathematics - Rings and Algebras; Operator Algebras (math.OA)

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.