A Galois correspondence for compact group actions on C ⁎-algebras

Abstract

In this paper, we prove a Galois correspondence for compact group actions on C ⁎-algebras in the presence of a commuting minimal action. Namely, we show that there is a one-to-one correspondence between the C ⁎-subalgebras that are globally invariant under the compact action and the commuting minimal action, that in addition contain the fixed point algebra of the compact action and the closed, normal subgroups of the compact group.