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arXiv · 2608.28772

Non-MF groups and non-finite full group C*-algebras

Caleb Eckhardt
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Abstract

Let $\Gamma$ be a property (T) group admitting an injective, non-surjective endomorphism and let $G$ be the associated ascending HNN-extension. Let $W=\left(\bigoplus_{G/\Gamma} \mathbb{Z}/2\mathbb{Z}\right) \rtimes G.$ We show that $W$ is not an MF group and that $C^*(G)$ is not a finite C*-algebra. The ideas and proofs were generated by ChatGPT 5.6 Sol, we have only refined their arguments in a hopefully more palatable form.

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Caleb Eckhardt. 2026-08-28. Non-MF groups and non-finite full group C*-algebras. https://arxiv.org/abs/2608.28772

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