Irreducible representations of nilpotent groups generate classifiable C*-algebras

TL;DR

This paper demonstrates that C*-algebras generated by irreducible representations of finitely generated nilpotent groups are classifiable by their Elliott invariants, expanding understanding of their structure and classification.

Contribution

It proves these C*-algebras satisfy the universal coefficient theorem and are classifiable within a broad class of nuclear C*-algebras, linking representation theory and operator algebra classification.

Findings

C*-algebras from irreducible representations satisfy the UCT.

These algebras are classifiable by Elliott invariants.

They are central cutdowns of twisted group C*-algebras with trivial cocycles.

Abstract

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.