Date of this Version
Bull. Aust. Math. Soc. 90 (2014), 121–133; doi:10.1017/S0004972713001111
We show Exel’s tight representation of an inverse semigroup can be described in terms of joins and covers in the natural partial order. Using this, we show that the C*-algebra of a finitely aligned category of paths, developed by Spielberg, is the tight C*-algebra of a natural inverse semigroup. This includes as a special case finitely aligned higher-rank graphs: that is, for such a higher-rank graph Ʌ, the tight C* -algebra of the inverse semigroup associated to Ʌ is the same as the C*-algebra of Ʌ.