UCT-Kirchberg algebras have nuclear dimension one

TL;DR

This paper proves that all Kirchberg algebras in the UCT class have nuclear dimension one, using techniques from 2-graph algebras and direct limit constructions, advancing the understanding of their structural properties.

Contribution

It establishes that Kirchberg algebras in the UCT class have nuclear dimension one, a significant step in classifying their structural complexity.

Findings

Kirchberg 2-graph algebras with trivial K0 and finite K1 have nuclear dimension 1

Every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras

Main theorem confirms nuclear dimension 1 for all such algebras

Abstract

We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial $K_0$ and finite $K_1$ have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.