×

Irreducible representations of nilpotent groups generate classifiable \(C^*\)-algebras. (English) Zbl 1365.46052

Summary: We show that \(C^*\)-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these algebras are classifiable by their Elliott invariants within the class of unital, simple, separable, nuclear \(C^*\)-algebras with finite nuclear dimension that satisfy the universal coefficient theorem. We also show that these \(C^*\)-algebras are central cutdowns of twisted group \(C^*\)-algebras with homotopically trivial cocycles.

MSC:

46L35 Classifications of \(C^*\)-algebras
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
PDFBibTeX XMLCite
Full Text: DOI arXiv