Journal of Noncommutative Geometry
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Published online: 2018-10-30
On reduced twisted group C*-algebras that are simple and/or have a unique traceErik Bédos and Tron Omland (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