\(C^*\)-algebras associated with rotation groups and characters (Q1066426)

Let T be the circle group, \(\theta\) a countable discrete abelian group and \(\sigma\) a character of G. Then one can define the \(C^*\)-crossed product \(G\times_{{\tilde \sigma}}C(T)\) which generalizes rotation \(C^*\)-algebras studied before by a number of authors. The authors study a larger class of \(C^*\)-algebras defined by generators with a \(\sigma\)- twisted commutation property. A description of such algebras as twisted \(C^*\)-crossed products leads to information on centre, ideal lattice, primitive ideal space and tracial functions. It also gives a characterization of simplicity and a classification under liminarity conditions. The subclass corresponding to faithful characters is classified up to isomorphism.