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A Galois Correspondence for Reduced Crossed Products of Simple $\text{C}^{\ast }$-algebras by Discrete Groups
Published online by Cambridge University Press: 07 January 2019
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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- © Canadian Mathematical Society 2018
Footnotes
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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