Article contents
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.
- Type
- Research Article
- Information
- Copyright
- © Cambridge University Press, 2015
References
- 1
- Cited by