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On conjugacy of subalgebras in graph C*-algebras. II

Part of: Algebraic number theory: global fields Selfadjoint operator algebras

Published online by Cambridge University Press:  09 December 2022

Tomohiro Hayashi ,
Jeong Hee Hong  and
Wojciech Szymański
Tomohiro Hayashi
Affiliation:
Nagoya Institute of Technology, Gokiso-cho,Showa-ku, Nagoya, Aichi 466–8555, Japan (hayashi.tomohiro@nitech.ac.jp)
Jeong Hee Hong
Affiliation:
Department of Mathematics and Computer Science, The University of Southern Denmark, Campusvej 55, DK–5230 Odense M, Denmark (hongjh@imada.sdu.dk; szymanski@imada.sdu.dk)
Wojciech Szymański
Affiliation:
Department of Mathematics and Computer Science, The University of Southern Denmark, Campusvej 55, DK–5230 Odense M, Denmark (hongjh@imada.sdu.dk; szymanski@imada.sdu.dk)
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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 ${\mathcal {D}}_E$ 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

Graph C*-algebraMASAautomorphism

MSC classification

Primary: 46L05: General theory of $C^*$-algebras 46L40: Automorphisms 11R04: Algebraic numbers; rings of algebraic integers
Secondary: 11R21: Other number fields
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 4 , November 2022 , pp. 1162 - 1182
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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