Cuntz–Krieger algebras and one-sided conjugacy of shifts of finite type and their groupoids

Kevin Aguyar Brix, Toke Meier Carlsen

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A one-sided shift of finite type (XAA) 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, (XAA) 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.
Original languageEnglish
Pages (from-to)289-298
Number of pages10
JournalJournal of the Australian Mathematical Society
Publication statusPublished - 21 Dec 2020


  • Shifts of finite type
  • groupoids
  • Cuntz-Krieger algebras


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