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

  • Jan Cameron (a1) and Roger R. Smith (a2)
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 $A\rtimes _{\unicode[STIX]{x1D6FC},r}^{\unicode[STIX]{x1D70E}}G$ .

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Author J. C. was partially supported by Simons Collaboration Grant for Mathematicians #319001. Author R. S. was partially supported by Simons Collaboration Grant for Mathematicians #522375.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
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