Graph C*-algebras and orbit equivalence

Operator Algebra Seminar by Toke Meier Carlsen

Recently Matsumoto and Matui proved that if A and B are two irreducible square matrices with entries in {0,1}, then the corresponding two-sided topological Markov shifts are flow equivalent if and only if there is an isomorphism between the stabilizations of the Cuntz-Krieger algebras of A and B which maps the canonical maximal abelian subalgebra onto each other. An important ingredient of their proof of this result is a theorem of Matsumoto which says that there is an isomorphism between the Cuntz-Krieger algebras of A and B which maps the canonical maximal abelian subalgebra onto each other if and only if the one-sided topological Markov shifts corresponding to A and B are continuously orbit equivalent.

In this talk, I will report on my attempt with Nathan Brownlowe and Michael Whittaker from the University of Wollongong to generalise the latter result to arbitrary graph algebras.