arXiv subjects

Ben Bouwen

Publications and source records attributed to Ben Bouwen.

2 recordsLinked to original sources

arXiv2025

Embeddings into the ultrapower of the Jiang-Su algebra

We study existence of embeddings into ultrapowers of the Jiang-Su algebra $\mathcal{Z}$ and the Razak-Jacelon algebra $\mathcal{W}$. More specifically, we show that the cone over any separable $C^*$-algebra embeds into the ultrapowers of both $\mathcal{Z}$ and $\mathcal{W}$. We also show that the result for $\mathcal{Z}$ generalizes to separable and exact continuous fields of $C^*$-algebras for which one of the fibers embeds into the ultrapower of $\mathcal{Z}$, if this fiber is suitably well-behaved.

math.OA↗

arXiv2024

A unified approach for classifying simple nuclear $C^\ast$-algebras

We provide a new proof of the Kirchberg--Phillips theorem by adapting the framework laid out by Carrión--Gabe--Schafhauser--Tikuisis--White for classifying separable simple unital nuclear stably finite $\mathcal Z$-stable $C^\ast$-algebras satisfying the UCT. Not only does this give a unified approach to classifying stably finite and purely infinite $C^\ast$-algebras, in contrast to the other proofs of the Kirchberg--Phillips theorem, our proof does not rely on Kirchberg's Geneva Theorems, but instead implies them as corollaries (for nuclear $C^\ast$-algebras).

math.OA↗