UCT-Kirchberg algebras have nuclear dimension one

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.

21 pages. Version 2: reference [2] has been added, and the discussion in the introduction updated; a small but important typo has been corrected in the definition of the graph E_T. Version 3: Some typo's corrected and references updated; reference [2] corrected as we had accidentally omitted one of the authors' names in the previous version (sorry Aaron!); this version to appear in Adv. Math