On conjugacy of subalgebras in graph <i>C</i>*-algebras. II

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 new proof non-inner the diagonal MASA ${\mathcal {D}}_E$ its non-trivial image under quasi-free automorphism, where $E$ is finite transitive graph. Changing graphs representing algebras, this result applies some non automorphisms as well. Then, exhibit large class Cuntz algebra {O}}_n$ that are not conjugate {D}}_n$ .