On Conjugacy of Subalgebras of Graph C*-Algebras

Abstract

The problem of inner vs outer conjugacy of subalgebras of certain graph C * -algebras is investigated. 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 * -algebraThat is, the two MASAs D E and α(D E ) of C * (E) are outer but not inner conjugate. For the Cuntz algebras O n , we find a criterion which guarantees that a polynomial automorphism moves the canonical UHF subalgebra to a non-inner conjugate UHF subalgebra. The criterion is phrased in terms of rescaling of trace on diagonal projections.