A Galois Correspondence for Reduced Crossed Products of Simple $\text{C}^{\ast }$-algebras by Discrete Groups. (October 2019)

• Record Type: Journal Article
• Authors: Cameron, Jan; Smith, Roger R.
• Is Part Of: Canadian journal of mathematics. Volume 71:Number 5(2019)
• Page Start: 1103
• Page End: 1125
• Publication Date: 2019-10
• Subjects: 46L55, -- 46L40; C∗ -algebra, -- group, -- crossed product, -- bimodule, -- reduced, -- twisted; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2018-014-6
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: Let a discrete group $G$ act on a unital simple $\text{C}^{\ast }$ -algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A\rtimes _{\unicode[STIX]{x1D6FC}, r}H$ between subgroups of $G$ and $\text{C}^{\ast }$ -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 $A\rtimes _{\unicode[STIX]{x1D6FC}, r}^{\unicode[STIX]{x1D70E}}G$ .