@inproceedings{828d185de0cb439c874f2ae2e39c4592,

title = "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*-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.",

keywords = "C-functions, Cuntz algebra, MASA, S-functions, UHF-subalgebra, automorphism, graph C -algebra, inner and outer conjugacy",

author = "Mikkelsen, {Sophie Emma} and Wojciech Szymanski and Hong, {Jeong Hee} and Tomohiro Hayashi",

year = "2019",

doi = "10.1007/978-3-030-34072-8_17",

language = "English",

isbn = "978-3-030-34071-1",

series = "Trends in Mathematics",

publisher = "Birkh{\"a}user Verlag",

pages = "163--173",

booktitle = "Geometric Methods in Physics XXXVII :",

address = "Switzerland",

note = "XXXIX Workshop on Geometric Methods in Physics ; Conference date: 01-07-2018 Through 07-07-2018",

}