Gauge freeness for Cuntz-Pimsner algebras

To every $C^{\ast }$ correspondence over a $C^{\ast }$-algebra one can associate a Cuntz-Pimsner algebra generalizing crossed product constructions, graph $C^{\ast }$-algebras, and a host of other classes of operator algebras. Cuntz-Pimsner algebras come equipped with a `gauge action’ by the circle group and its finite subgroups. For unital Cuntz-Pimsner algebras, we derive necessary and sufficient conditions for the gauge actions (by either the circle or its closed subgroups) to be free.