# C*-simplicity and the unique trace property for discrete groups

@article{Breuillard2014CsimplicityAT,
title={C*-simplicity and the unique trace property for discrete groups},
author={Emmanuel Breuillard and Mehrdad Kalantar and Matthew Kennedy and Narutaka Ozawa},
journal={Publications math{\'e}matiques de l'IH{\'E}S},
year={2014},
volume={126},
pages={35-71}
}
• Published 9 October 2014
• Mathematics
• Publications mathématiques de l'IHÉS
A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently obtained by the second and third named authors. In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to take the study of C*-simplicity a step further, and in addition to settle the longstanding open…
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