A Galois Correspondence for Reduced Crossed Products of Simple $\text{C}^{* }$-algebras by Discrete Groups. (October 2019) - Cameron, Jan; Smith, Roger R.
Abstract: Let a discrete group $G$ act on a unital simple $\text{C}^{* }$ -algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A\rtimes _{\unicode[STIX]{x1D6FC}, r}H$ between subgroups of $G$ and $\text{C}^{* }$ -algebras $B$ satisfying $A\subseteq B\subseteq A\rtimes _{\unicode[STIX]{x1D6FC}, r}G$, where $A\rtimes _{\unicode[STIX]{x1D6FC}, r}G$ denotes the reduced crossed product. For a twisted dynamical system $(A, G, \unicode[STIX]{x1D6FC}, \unicode[STIX]{x1D70E})$, we also prove the corresponding result for the reduced twisted crossed product $A\rtimes _{\unicode[STIX]{x1D6FC}, r}^{\unicode[STIX]{x1D70E}}G$ .