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arXiv · 1406.2045

UCT-Kirchberg algebras have nuclear dimension one

Efren Ruiz·Aidan Sims·Adam P. W. Sørensen
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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.

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Efren Ruiz, Aidan Sims, Adam P. W. Sørensen. 2014-06-09. UCT-Kirchberg algebras have nuclear dimension one. https://arxiv.org/abs/1406.2045

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