On Conjugacy of MASAs in Graph C*-Algebras

Original · EN

For a large class of finite graphs E, we show that whenever α is a vertex-fixing quasi-free automorphism of the corresponding graph C*-algebra C*(E) such that α(Dₑ) ≠Dₑ, where Dₑ is the canonical MASA in C*(E), then α(Dₑ)≠ wDₑ w* for all unitaries w∈ C*(E). That is, the two MASAs Dₑ and α(Dₑ) of C*(E) are outer but not inner conjugate. Passing to an isomorphic C*-algebra by changing the underlying graph makes this result applicable to certain non quasi-free automorphisms as well.