Geodesic
A Galois Correspondence for Reduced Crossed Products of Simple $\text{C}^{\ast }$-algebras by Discrete Groups
Canadian journal of mathematics, Tome 71 (2019) no. 5, pp. 1103-1125

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DOI

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 $A\rtimes _{\unicode[STIX]{x1D6FC},r}^{\unicode[STIX]{x1D70E}}G$.
DOI : 10.4153/CJM-2018-014-6
Mots-clés : C∗ -algebra, group, crossed product, bimodule, reduced, twisted 
Cameron, Jan; Smith, Roger R. A Galois Correspondence for Reduced Crossed Products of Simple $\text{C}^{\ast }$-algebras by Discrete Groups. Canadian journal of mathematics, Tome 71 (2019) no. 5, pp. 1103-1125. doi: 10.4153/CJM-2018-014-6
@article{10_4153_CJM_2018_014_6,
     author = {Cameron, Jan and Smith, Roger R.},
     title = {A {Galois} {Correspondence} for {Reduced} {Crossed} {Products} of {Simple} $\text{C}^{\ast }$-algebras by {Discrete} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {1103--1125},
     year = {2019},
     volume = {71},
     number = {5},
     doi = {10.4153/CJM-2018-014-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2018-014-6/}
}
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