On the nuclear dimension of certain UCT-Kirchberg algebras

TL;DR

This paper determines that certain UCT-Kirchberg algebras with torsion-free K_1 groups have nuclear dimension 1, advancing understanding of their structural properties in operator algebra theory.

Contribution

It proves that all UCT-Kirchberg algebras with torsion-free K_1 groups have nuclear dimension 1, partially answering a question posed by Winter and Zacharias.

Findings

UCT-Kirchberg algebras with torsion-free K_1 have nuclear dimension 1

Provides partial answer to the nuclear dimension question for UCT-Kirchberg algebras

Advances classification theory of nuclear C*-algebras

Abstract

We give a partial answer to the question for the precise value of the nuclear dimension of UCT-Kirchberg algebras raised by W. Winter and J. Zacharias. It is shown that every Kirchberg algebra in the UCT-class with torsion free $K_1$-group has nuclear dimension 1.