The dynamics of a one-sided subshift X can be modeled by a set of partially defined bijections. From this data we define an inverse semigroup SX and show that it has many interesting properties. We prove that the Carlsen–Matsumoto C*-algebra OX associated to X is canonically isomorphic to Exel's tight C*-algebra of SX. As one consequence, we obtain that OX can be written as a partial crossed product of a commutative C*-algebra by a countable group.

C*-algebras, Inverse semigroups, Subshifts, Tight representations
Journal of Algebra

Starling, C. (2016). Inverse semigroups associated to subshifts. Journal of Algebra, 463, 211–233. doi:10.1016/j.jalgebra.2016.06.014