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arXiv · 2003.02120

On Conjugacy of Subalgebras of Graph C*-Algebras

Tomohiro Hayashi·Jeong Hee Hong·Sophie Emma Zegers·Wojciech Szymański
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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(\D_E)\neq\D_E, where \D_E is the canonical MASA in C*(E), then α(\D_E)\neq w\D_E w^* for all unitaries w\in C*(E). That is, the two MASAs \D_E and α(\D_E) of C*(E) are outer but not inner conjugate. Passing to an isomorphic C*-algebra by changing the underlying graph makes this result applicable to certain non quasi-free automorphisms as well. 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.

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Tomohiro Hayashi, Jeong Hee Hong, Sophie Emma Zegers, Wojciech Szymański. 2020-03-02. On Conjugacy of Subalgebras of Graph C*-Algebras. https://arxiv.org/abs/2003.02120

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