Subshift semigroups

Abstract

Given a one-sided subshift $X$ on a finite alphabet, we consider the semigroup $S_X=L_X\cup \{0\}$, where $L_X$ is the language of $X$, equipped with the multiplication operation given by concatenation, when allowed, and set to vanish otherwise. We then study the inverse hull $H(S_X)$, relating it with C*-algebras that have been discussed in the literature in association with subshifts.