A Galois correspondence for reduced crossed products of unital simple C${}^{\ast }$-algebras by discrete groups

Abstract

Let a discrete group $G$ act on a unital simple C${}^{\ast }$-algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A{⋊}_{\alpha ,r}H$ between subgroups of $G$ and C${}^{\ast }$-algebras $B$ satisfying $A\subseteq B\subseteq A{⋊}_{\alpha ,r}G$, where $A{⋊}_{\alpha ,r}G$ denotes the reduced crossed product. For a twisted dynamical system $(A,G,\alpha ,\sigma )$, we also prove the corresponding result for the reduced twisted crossed product $A{⋊}_{\alpha ,r}^{\sigma }G$.

As pointed out to us by Prof. Yuhei Suzuki, there is an error in Lemma 2.9 of v1. Lemmas 2.8 and 2.9 in v1 are replaced by Lemmas 2.8-2.12 in v2. The main results of the paper are unchanged. A correction will be sent to Canad. J. Math

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