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

Abstract

We show that the twisted group C${}^{\ast }$-algebra associated with a discrete FC-hypercentral group is simple (resp. has a unique tracial state) if and only if Kleppner's condition is satisfied. This generalizes a result of J. 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.

16 pages. Some minor changes, mostly in subsection 2.3; two references added

References in corpus (1)

• Primeness and primitivity conditions for twisted group $C^{\ast }$-algebras

Cited by in corpus (1)

• C*-irreducibility for reduced twisted group C*-algebras