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On Conjugacy of Subalgebras of Graph C*-Algebras

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Geometric Methods in Physics XXXVII

Part of the book series: Trends in Mathematics ((TM))

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) ̸= wDEw * for all unitaries w ∈ 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.

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Hayashi, T., Hong, J.H., Mikkelsen, S.E., Szymański, W. (2019). On Conjugacy of Subalgebras of Graph C*-Algebras. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXVII. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34072-8_17

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