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arXiv · 2201.08009

On Conjugacy of Subalgebras in Graph $C^*$-Algebras. II

Tomohiro Hayashi·Jeong Hee Hong·Wojciech Szymański
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Abstract

We apply a method inspired by Popa's intertwining-by-bimodules technique to investigate inner conjugacy of MASAs in graph $C^*$-algebras. First we give a new proof of non-inner conjugacy of the diagonal MASA ${\mathcal D}_n$ to its non-trivial image under a quasi-free automorphism, where $E$ is a finite transitive graph. Changing graphs representing the algebras, this result applies to some non quasi-free automorphisms as well. Then we exhibit a large class of MASAs in the Cuntz algebra ${\mathcal O}_n$ that are not inner conjugate to the diagonal ${\mathcal D}_n$.

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Tomohiro Hayashi, Jeong Hee Hong, Wojciech Szymański. 2022-01-20. On Conjugacy of Subalgebras in Graph $C^*$-Algebras. II. https://arxiv.org/abs/2201.08009

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