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Published in:
2019 | OriginalPaper | Chapter
On Conjugacy of Subalgebras of Graph C*-Algebras
Authors : Tomohiro Hayashi, Jeong Hee Hong, Sophie Emma Mikkelsen, Wojciech Szymański
Published in: Geometric Methods in Physics XXXVII
Publisher: Springer International Publishing
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(DE) ≠ DE where DE is the canonical MASA in C*(E), then α(DE) ≠ ωDEω* for all unitaries ω ∈ C* (E). That is, the two MASAs DE and α(DE) of C*(E) are outer but not inner conjugate. For the Cuntz algebras On, 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.