On Conjugacy of Subalgebras of Graph C*-Algebras

摘要

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*-algebra C*(E) such that α(D_E) ≠ D_E, where D_E is the canonical MASA in C*(E), then α(D_E) ≠ wD_(Ew)* for all unitaries w ∈ C*(E). That 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 sub-algebra to a non-inner conjugate UHF subalgebra. The criterion is phrased in terms of rescaling of trace on diagonal projections.