A one-sided shift of finite type (XA,σA) determines on the one hand a Cuntz–Krieger algebra OA with a distinguished abelian subalgebra DA and a certain completely positive map τA on OA . On the other hand, (XA,σA) determines a groupoid GA together with a certain homomorphism ϵA on GA . We show that each of these two sets of data completely characterizes the one-sided conjugacy class of XA . This strengthens a result of Cuntz and Krieger. We also exhibit an example of two irreducible shifts of finite type which are eventually conjugate but not conjugate. This provides a negative answer to a question of Matsumoto of whether eventual conjugacy implies conjugacy.
- Shifts of finite type
- Cuntz-Krieger algebras