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

Tomohiro Hayashi, Jeong Hee Hong*, Wojciech Szymanski

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


We apply a method inspired by Popa's intertwining-by-bimodules technique to investigate inner conjugacy of MASAs in graph -algebras. First, we give a new proof of non-inner conjugacy of the diagonal MASA to its non-trivial image under a quasi-free automorphism, where 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 that are not inner conjugate to the diagonal.

Original languageEnglish
JournalProceedings of the Edinburgh Mathematical Society
Issue number4
Pages (from-to)1162-1182
Publication statusPublished - Nov 2022


  • graph C*-algebra
  • MASA
  • automorphism
  • -algebra
  • Graph C


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