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On twisted group $C^{\ast }$-algebras associated with FC-hypercentral groups and other related groups

Published online by Cambridge University Press:  01 June 2015

ERIK BÉDOS  and
TRON OMLAND
ERIK BÉDOS
Affiliation:
Institute of Mathematics, University of Oslo, P.B. 1053 Blindern, 0316 Oslo, Norway email bedos@math.uio.no
TRON OMLAND
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, PO Box 871804, Tempe, AZ 85287-1804, USA email omland@asu.edu
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Abstract

We show that the twisted group $C^{\ast }$-algebra associated with a discrete FC-hypercentral group is simple (respectively, has a unique tracial state) if and only if Kleppner’s condition is satisfied. This generalizes a result of Packer for countable nilpotent groups. We also consider a larger class of groups, for which we can show that the corresponding reduced twisted group $C^{\ast }$-algebras have a unique tracial state if and only if Kleppner’s condition holds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 6 , September 2016 , pp. 1743 - 1756
Copyright
© Cambridge University Press, 2015 

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