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On conjugacy of subalgebras in graph C*-algebras. II
Published online by Cambridge University Press: 09 December 2022
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 ${\mathcal {D}}_E$
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 ${\mathcal {D}}_n$
.
Keywords
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 4 , November 2022 , pp. 1162 - 1182
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
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