Inclusions of simple C⁎-algebras arising from compact group actions

Inclusions of operator algebras have long been studied. In particular, inclusions arising from actions of compact groups on factors were studied by Izumi-Longo-Popa and others. The correspondence between intermediate subfactors and subgroups is called the Galois correspondence. Analogues for actions on C^⁎-algebras have been studied by Izumi, Cameron-Smith, Peligrad, and others. In this article, we give examples of compact group actions on simple C^⁎-algebras for which the Galois correspondence holds.