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arXiv · 2610.02174

Unital embeddings of the Jiang--Su algebra are not unique

Matteo Pagliero
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Abstract

We show that the canonical embeddings of the Jiang--Su algebra $\mathcal Z$ into the universal unital free product $\mathcal Z \ast_{\mathbb C}\mathcal Z$ are not approximately unitarily equivalent. This answers one of the $99$ problems in the list of Schafhauser, Tikuisis, and White. By contrast, we prove that any two such embeddings into a simple, unital, monotracial $\mathrm{C}^\ast$-algebra with strict comparison by the unique trace are strongly asymptotically unitarily equivalent.

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Matteo Pagliero. 2026-10-01. Unital embeddings of the Jiang--Su algebra are not unique. https://arxiv.org/abs/2610.02174

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