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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
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.
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- Research Article
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- © Cambridge University Press, 2015
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