Journal of Noncommutative Geometry


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Volume 12, Issue 3, 2018, pp. 947–996
DOI: 10.4171/JNCG/295

Published online: 2018-10-30

On reduced twisted group C*-algebras that are simple and/or have a unique trace

Erik Bédos[1] and Tron Omland[2]

(1) University of Oslo, Norway
(2) University of Oslo, Norway

We study the problem of determining when the reduced twisted group C*-algebra associated with a discrete group $G$ is simple and/or has a unique tracial state, and present new sufficient conditions for this to hold. One of our main tools is a combinatorial property, that we call the relative Kleppner condition, which ensures that a quotient group $G/H$ acts by freely acting automorphisms on the twisted group von Neumann algebra associated to a normal subgroup$ $H. We apply our results to different types of groups, e.g. wreath products and Baumslag-Solitar groups.

Keywords: Reduced twisted group C*-algebra, simplicity, unique trace

Bédos Erik, Omland Tron: On reduced twisted group C*-algebras that are simple and/or have a unique trace. J. Noncommut. Geom. 12 (2018), 947-996. doi: 10.4171/JNCG/295