Non-minimal free actions of countable abelian groups on the circle yield quasidiagonal nuclear non-simple C*-algebras with stable rank one, unique trace, bounded nuclear dimension, and computable ordered K-theory when the group is Z^d.
Navas.Groups of Circle Diffeomorphisms
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Crossed product C*-algebras associated with non-minimal actions on the circle
Non-minimal free actions of countable abelian groups on the circle yield quasidiagonal nuclear non-simple C*-algebras with stable rank one, unique trace, bounded nuclear dimension, and computable ordered K-theory when the group is Z^d.